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its density. 15. A wooden raft 5 ft. long and 4 ft. wide floats in water. When a person steps on the raft it sinks 1.5 inches deeper into the water. Calculate the person’s weight. 16. A cork of volume 60 c.c. and density 0.24 gm. per c.c. floats in a liquid of density 0.85 gm. per c.c. Find the least weight required to sink it. 17. What volume of lead of density 11.2 gm. per c.c. will be required to sink a piece of wood in water, the weight of the wood being 425 gm. and its volume 556 C.C.? 18. A block of wood of volume 100 c.c. floats in a liquid of specific gravity 1.2 with 75 c.c. immersed. Calculate the density of the wood. 19. A wooden hydrometer sinks in water to a depth of 1 8 cm. and in a liquid to a depth of 1 4 cm. What is the specific gravity of the liquid? 20. A hydrometer sinks in water to a depth of 1 5 cm. How far would it sink in a liquid whose specific gravity Is 0.80? 21. A hydrometer sinks to a depth of 1 2 cm. in a liquid whose specific gravity is 1.7. To what depth would it sink in water? 22. A piece of wood whose volume is 1 50 c.c. floats with of its volume submerged in water. Find its mass. 23. A piece of wood whose mass is 75.0 gm. floats in water with ^ of its volume above the surface. Find its volume. 24. A piece of cork of density 0.25 gm. per c.c. floats in a liquid of density 1.2 gm. per c.c. What proportion of the volume of the cork will be immersed? 25. An object floats in water with half its volume submerged. How much will be submerged when it floats in a liquid of specific gravity 1.5? 26. To what depth will a block of wood 20 cm. high and of density 0.63 gm. per c.c. sink in a liquid of density 0.90 gm. per c.c.? • 33 CHAPTER 5 EXPERIMENTS ON MECHANICS INTRODUCTION Before proceeding with the following experiments the student should review the following
techniques used in measurement. A. — Use of the ruler 1. Avoid using the ends of the ruler. 2. Place your eye directly above the point where the reading is to be taken to avoid the error due to parallax. B / Measuring Length with a Fig. 5:1 Ruler—How to Avoid the Error Due to Parallax. Fig. 5:2 Measuring Volume with a Graduated Cylinder, B, — Use of the graduated cylinder Place your eye directly opposite the centre of the meniscus curve. Take the reading at this level. C. — Use of the balance 1. Clean and level the balance. 2. Support the beam of the balance on the knife-edge as demonstrated by the instructor. 3. Adjust for zero reading with all weights removed. Note that in all readings the pointer should swing an equal number of divisions on either side of the zero mark on the scale. Do not wait for the pointer to come to rest. 4. Place object to be weighed on the centre of the left pan of the balance. 5. Commencing with a weight that is definitely too heavy on the right- 34 EXPERIMENTS ON MECHANICS A B Fisher Scientific Co. Canadian laboratory Supplies Ltd. Fig. 5:3 The Balances A—Triple-beam balance. B— Equal-arm balance and box of weights. hand pan of the equal-arm balance (or on the arm of the triple-beam balance), systematically reduce the weight until balance is attained. 6. Total the weights used. 7. Disengage the knife-edge and return all weights to their box or to their zero position. EXPERIMENT 1 To determine the density of a regular solid. (Ref. Sec. 1:5) Apparatus Rectangular solid, ruler (graduated in mm.), balance. 1. Carefully measure to the nearest millimetre the length, width and 35 Chap. 5 MECHANICS thickness of a rectangular solid.* Record your measurements, and calculate the volume of the object in cubic centimetres. 2. Determine the mass of the object and record it in grams. Observations = Length = Width Thickness = Mass =: cm. cm. cm. gm. Calculations 1. What is the volume of the object? 2. Determine the mass of one cubic centimetre. 3. What is the average of the results obtained by the class? Conclusion What is the density of this material?
Questions 1. What is the correct value for the density of this material? (Table P-21). 2. Express the difference between the class average and the true value as a percentage of the true value. This is a measure of the experimental error. 3. Suggest sources of experimental error. * Note The density of other regular solids, such as a cylinder (Volume = 77 h), or a sphere (Volume = - tt 4 3 may be determined in a similar way (Fig. 5:4). EXPERIMENT 2 To determine the density of an irregular solid (rubber stopper), (Ref. Sec, 1:5) 36 EXPERIMENTS ON MECHANICS Apparatus Rubber stopper, thread, graduated cylinder, water, balance. Method 1. Determine the mass of the object and record it in grams. 2. Half fill a graduated cylinder with water. Note and record the Tie a thread to the object and carefully volume of the water. is completely immersed. Note and lower it into the water until it record the final volume of the water and object. Determine the volume of the object and record it in cubic centimetres. Observations Mass of object Initial volume of water Final volume of water and object.'. Volume of object'= = = rr gm. c.c. c.c. c.c. Conclusion What is the density of this material? Question Why should the object be weighed before its volume is determined? EXPERIMENT 3 To determine the density of a liquid by measurement, (Ref. Sec. 1:5) Apparatus Beaker, graduated cylinder, balance, liquid (water, alcohol, etc.). Method 1. Determine the mass of a clean dry beaker. 2. Add about 50 c.c.^of the liquid to the beaker, weigh, and hence determine the mass of the liquid used. 3. Pour the liquid into a graduated cylinder and determine its volume. Observations = Mass of beaker Mass of beaker plus liquid = =.'. Mass of liquid Volume of liquid gm. gm. gm. c.c. Calculations Determine the mass of one cubic centimetre. What is the average of the results obtained by the class? Conclusion What is the density of this liquid? 37 Chap. 5 MECHANICS Questions 1. What is the correct value for the density of this liquid? (Table p. 21) 2. Calculate the percentage error.
3. Suggest sources of experimental error. 4. If the balance at your disposal is suitable, a graduated cylinder, instead of a beaker, could be used in steps 1 and 2 in the above experiment. Why should this tend to reduce the experimental error? EXPERIMENT 4 To determine the specific gravity of a liquid by means of the specific gravity bottle. (Ref. Sec. 1:7) Apparatus Specific-gravity bottle, water, balance, liquid (carbon tetrachloride, alcohol, etc.) X Fig. 5:6 Method 1. Carefully clean and dry the bottle. Determine its mass. 2. Fill completely with the liquid whose specific gravity is to be Insert the stopper, wipe off any excess liquid that determined. exudes through the opening. Determine the mass of the bottle plus the liquid. 3. Pour out the liquid. Rinse out the bottle with water. Fill the bottle completely with water. Determine the mass of the bottle plus the water. 38 EXPERIMENTS ON MECHANICS Observations = Mass of specific-gravity bottle empty Mass of specific-gravity bottle full of liquid = = Mass of specific-gravity bottle full of water = =.’. Mass of water Mass of liquid gm. gm. gm. gm. gm. Conclusion What is the specific gravity of the liquid? Questions 1. Define specific gravity. 2. Calculate the percentage error. 3. Suggest sources of experimental error. 4. What is the purpose of the hole through the centre of the stopper of the specific-gravity bottle? EXPERIMENT 5 To demonstrate Archimedes' Principle. (Ref. Sec. 1:11) Apparatus Balance, bucket and cylinder apparatus, beaker, water. Method 1. Hook the cylinder A on the bottom of the bucket B. Suspend them from the hook on the balance. Adjust the weights until the balance is in equilibrium. 2. Completely immerse the cylinder in a beaker of water. Be sure that the cylinder does not touch the bottom or sides of the beaker. Note the effect on the equilibrium. 3. Carefully add water to the bucket until it is completely full. Again note the effect on the equilibrium. 39 Chap. 5 MECHANICS Observations 1. What was observed when the cylinder was completely immersed in the water? 2. What was observed when the bucket was filled with water? Conclusions 1. Why was the equilibrium disturbed
in step 2? 2. Why was the equilibrium restored in step 3? 3. State Archimedes’ Principle. Questions 1. Why do objects apparently weigh less when immersed in a liquid? 2. What would be the effect of immersing the object in a denser liquid? EXPERIMENT 6 Alternative method to demonstrate Archimedes' Principle. (Ref. Sec. 1:11) Apparatus Balance, object (glass stopper), beaker, overflow can, catch bucket, water, several other liquids (alcohol, carbon tetrachloride, brine, etc.) Method 1. Suspend the object from the hook on the balance. Determine its mass in air. 40 EXPERIMENTS ON MECHANICS 2. Completely immerse the object in a beaker of water. Be sure that it does not touch the beaker. Weigh the object while immersed in water. 3. Weigh a dry empty catch bucket. 4. Completely fill an overflow can with water. Let any excess water flow freely from the spout and discard it. Do not disturb the overflow can. Place the catch bucket under the spout. Carefully lower the object into the water and catch all of the overflow in the bucket. Weigh the catch bucket and overflow water. 5. Repeat the above using other liquids and fill in the table below. Observations Liquid Used Water Alcohol Carbon TETRAC H LORIDE Weight of object in air Weight of object in liquid.'. Apparent loss of weight in liquid Weight of empty catch bucket Weight of bucket plus displaced liquid.*. Weight of displaced liquid Conclusions 1. How does the apparent loss of weight compare with the weight of liquid displaced? 2. State Archimedes’ Principle. Questions 1. Why is a glass stopper an ideal solid to use in the above experiment? 2. What type of solid must be avoided? EXPERIMENT 7 To determine the specific gravity of a solid which is more dense than water using Archimedes' Principle. (Ref. Sec. 1:11) Apparatus Balance, beaker, water, thread, several solid objects more dense than water. Fig. 5:9 41 ). Chap. 5 MECHANICS Method 1. Suspend a solid object by a thread from the hook on the balance. Determine its weight in air. 2. Completely immerse the object in a beaker of water. Be sure that it Determine the weight
of the object does not touch the beaker. when immersed in water. 3. Repeat the above weighings for other objects supplied and fill in the table below. Observations Object Weight in Air Weight in Water Apparent Loss IN Weight 1. 2. 3. Calculations Weight of object in air = Apparent loss in weight = Weight of water displaced = gm. gm. gm. (Archimedes’ Principle) Specific gravity =.’. Specific gravity = Weight of object in air Weight of equal volume of water Conclusion What is the specific gravity of the object? Questions 1. Calculate the percentage error. 2. Suggest sources of experimental error. 3. Explain how the weight of an equal volume of water was deter- mined. 4. State the density of the above objects in the metric system of units. 5. Discuss advantages and disadvantages of this method for finding density compared with the method used formerly (Exp. 2) EXPERIMENT 8 To determine the specific gravity of a liquid using Archimedes' Principle. (Ref. Sec. 1 : 1 1 Apparatus Balance, glass stopper, thread, several beakers, water, liquid (alcohol, carbon tetrachloride, etc.). Method 1. Suspend the object by a thread from the hook on the balance. Determine its weight in air. 42 EXPERIMENTS ON MECHANICS 2. Immerse the object in a beaker of water, being careful not to let it touch the beaker. Determine the weight of the object when immersed in water. 3. Rinse the object in a reserve supply of the liquid whose specific gravity is to be determined. Immerse the object in a beaker of this liquid and again weigh. 4. Repeat for other liquids supplied. Weight of Object in Air Weight of Object in Water Weight of Object in Liquid Observations Liquid Used Alcohol Carbon tetrachloride Calculations Mass of water displaced = Mass of liquid displaced = Calculate the specific gravity of this liquid. gm. gm. Conclusion What is the specific gravity of the liquid used? Questions 1. Calculate the percentage error. 2. Suggest sources of error. 3. Explain how the mass of water displaced or of liquid displaced was obtained in the above experiment. 4. Why was it correct to say that the volumes of water displaced and of liquid displaced were equal? EXPERIMENT 9 To demonstrate the Principle of Flotation. (Ref. Sec. 1:12
) Apparatus Balance, paraffined wooden block, overflow can and catch bucket, water, other liquids. 43 Chap. 5 MECHANICS Method 1. Place the overflow can on the pan of the balance. Fill the overflow can to the spout with water (Exp. 6). Balance it. 2. Without adjusting the weights, and after placing the catch bucket under the spout of the overflow can, carefully lower the wooden block into the water. Let it float freely being careful not to let it touch the sides of the can. Note all changes that occur until the water ceases to flow. 3. Repeat this experiment using the other liquids provided. Observations Describe the changes in equilibrium that occurred. Conclusions 1. How does the mass of the floating block compare with the mass of liquid it displaces? 2. State the Principle of Flotation. Questions 1. Why was the block of wood used in the above experiment coated with a thin film of paraffin? 2. Why does a steel ship float? EXPERIMENT 10 To show the principle of the hydrometer, (Ref. Sec. 1:13) Apparatus Simple hydrometer (Fig. 4:6), two tall cylindrical vessels, water, other liquids. Method 1. Float the hydrometer in a cylinder of water, being careful that it does not touch the sides. Note the depth to which it sinks in the water. Calculate the mass of the hydrometer. 2. Rinse the hydrometer in a reserve supply of the liquid to be used. Then float the hydrometer in a cylinder of the liquid, again being careful not to let it touch the sides. Record the depth to which it sinks in the liquid. 3. Repeat part 2 for other liquids. Observations = 1. Depth to which hydrometer sinks in water 2. Depth to which hydrometer sinks in the liquid = Calculations Calculate the specific gravity of the liquid. 44. EXPERIMENTS ON MECHANICS Conclusions 1. What is the specific gravity of the liquid? 2. On what principle does the use of the hydrometer depend? Questions 1. How do you find the mass of the hydrometer? 2. How do you find the mass of the liquid displaced? 3. How is the depth that the hydrometer sinks related to the specific gravity of the liquid? 4. What is the use of the hydrometer? EXPERIMENT 11
To determine the specific gravity of a liquid using a hydrometer, (Ref. Sec. 1:13) Apparatus Several tall cylindrical vessels, several liquids (brine, alcohol, etc.), three hydrometers (one for heavy liquids, one for light liquids, one universal) Method 1. Float an appropriate hydrometer in a cylinder containing the liquid whose specific gravity is to be determined. Be careful not to let it touch the sides of the vessel. Determine the specific gravity by reading the hydrometer scale at the liquid surface level. 2. Repeat for other liquids. Note This hydrometer method can be used to check the specific gravities of liquids obtained in previous experiments. Observations Li^^uid Specific Gravity Conclusion State the specific gravity of each liquid used. Questions 1. Describe the construction of a hydrometer. 2. Why is the lower end of the hydrometer weighted (with mercury or lead shot)? 3. Is the flotation bulb on a hydrometer for low-density liquids larger or smaller than the bulb on a hydrometer for high-density liquids? Explain. 4. Why is the hydrometer scale graduated with the smallest readings at the top and the largest at the bottom? Explain. 45 UNIT II SOUND Describe the different ways in which the sound of this depth charge would be heard below and above the water, and why. star Newspaper Service CHAPTER 6 PRODUCTION AND TRANSMISSION OF SOUND 11:1 INTRODUCTION From earliest childhood our ears grow. accustomed to sounds about us : first the sound of our mother’s voice, then the : sounds of home, of nature, and the busy world. Our consideration of their nature rarely goes further than calling the sounds we dislike noises, and some of the more pleasant ones music. These, however, are often subjective definitions, 1 as can be seen from the fact that a “hot-rodder” may drive for miles in his unmuffled car and think the sound it is making is “music”, while he will hurriedly turn off the radio because of the “noise” Beethoven is making. I I I [ I I Man, in fact, has been interested in inventing devices for making music and noises for much longer than in investigating the nature of sound. References to musical instruments in the Old Testament date back to 4000 b.c. Remember I the story of Joshua and the walls of! Jericho
. Yet, although Aristotle and the early philosophers knew something of the physical nature of sound, it is only in the last four or five hundred years that a fuller understanding of it has been gained. [ j i The word sound has been used frequently already, but no effort has so far been made to define it. One definiit the sensation that results tion calls when the auditory nerve is stimulated, while another refers physical the to causes of this sensation, in terms of the three necessary agencies for any sound: a source, a medium and a receiver. It is this second definition of sound which will be our concern in this unit. 11:2 THE ORIGIN OF SOUND When we ring a bell, bow a string, or strike a tuning-fork, and bring each into contact with a light object such as a pith ball, the object moves away as if being struck regularly (Fig. 6:1). Some demonstrators may prefer to touch the sounding body to some water and note Fig. 6:1 Sounding Bodies Vibrate. the splash and waves set up. This is ample proof that the sounding body is vibrating, i.e., moving to and fro. It may be concluded that sound always 49 Chap. 6 SOUND originates in a rapidly vibrating body. of Only sufficiently rapid vibrations cause sound, but some vibrations, whether or not they emit sound, have other effects, such as the destruction buildings, bridges, or parts of moving machinery. To take one instance, the vibration set up by a body of troops marching would be sufficient to destroy some bridges and so troops marching across them have to break of vibratory motion is one of great importance. Obviously the study step. 11:3 A STUDY OF VIBRATORY MOTION (a) The Pendulum and Transverse Vibrations A simple device for demonstrating vibrations is the pendulum (Chap. 10, Exp. 1 ). This consists of a weight, called the bob, attached to the free end of a vertical cord, the other end of which is securely attached to a support (Fig. / \ \ \ \—V- \ \ / / / / / / / / Simple Pendulum in the Mean Position Amplitude of Vibration y- Movement of the Bob during one Vibration (Cycle) Fig. 6:2 Transverse Vibrations. 6:2). When the weight is drawn aside and allowed to swing, it will be -“seen the pendulum swings back �
e the same period. It is for this reason that the pendulum is used in For that physics as a timing device. reason also, it is the primary component of large clocks. Were you to experiment with pendulums of different lengths, the period of a short one would be less than It is for this reason that of a long one. that you shorten the pendulum of a frequently ; V PRODUCTION AND TRANSMISSION OF SOUND Sec. II:4 clock which loses time and lengthen it for one that gains. Another demonstration may be arranged using a long rnetal rod, clamped (b) LoyigitiuUnal Vibrations A coil spring with a weight attached is supported vertically from a strong support as in Fig. 6:3. When it is vibrated its pith centre, having a at in contact with one end as in Fig. 6:4. When the half of the rod farthest from the pith ball is stroked with a chamois shrill sound is coated with resin, ball a emitted. Meanwhile the pith ball is displaced in the direction of the axis of the rod, thus showing longitudinal vibrations, although these are too rapid to be seen in detail. These examples indiare cate characterized by motion back and forth along the length of the vibrating body. longitudinal vibrations that 11:4 MEDIA FOR THE TRANSMISSION OF SOUND The need for a material medium for the transmission of sound is studied in Fig. 6:3 Longitudinal Vibrations. so that the weight moves vertically by alternately stretching and compressing the spring, longitudinal vibrations result. Fortunately vibrations slow the are Fig. 6:4 Longitudinal Vibrations. enough to enable us to observe all the details as in the pendulum (Chap. 10, Exp. 2). Chap. 10, Exp. 3. There it will be found that as the air is removed from the belljar in which there is a vibrating bell (Fig. 6:5), the sound gradually becomes fainter. The bell is heard again when air is reintroduced into the bell- jar. Since Of THE UNIVERSITY Of ALBERTA 51 Chap. 6 SOUND from or towards the point of origin of the waves. Again, if part of our rope were chalk-marked, this part would be seen as a white line perpendicular to the length of the rope when the latter was vibrated at one end to set up a train of Electromagnetic waves waves along it
. (Sec. IV : 38), which include light waves, are also transverse in character. Fig. 6:6 shows the displacements of the particles of a medium transmitting a transverse wave. Particles at the crests (B, F, etc.) of the wave are undergoing a maximum displacement upwards, those at the bottom of the troughs (D, H, etc.) a maximum displacement downwards. Some terms used in wave motion follow: Amplitude is the maximum displacement from the mean position (BBi or DDi, etc.). Phase. Particles at the same distance from their mean positions and which are moving in the same direction are said to be in the same phase. Thus particles P and Q are in the same phase, as also are particles B and F. On the other hand, particles B and D are completely out of phase. Wave-Length is the distance, (/) usually expressed in centimetres or inches, between two consecutive particles in the same phase. Thus the distance BF between two adjacent crests, or the distance DH from one trough to the next, gives the wave-length of the disturbance. This we could see the vibrating bell throughout the entire experiment but could not hear the sound when there was no air present, we conclude that sound, unlike light, cannot travel through a vacuum. Sounds can also be conveyed through liquids and most solids. Thus the noise of the engines of a submarine can be picked up by underwater microphones, and the sound of vibrating telegraph wires can be clearly heard by an ear pressed against a telegraph post. 11:5 WAVE MOTION (a) Transverse Waves The disturbances set up by a vibrating body are propagated in the form of waves in the medium (Chap. 10, Exp. 4). A wave may be defined as a disturbance of any kind which travels without change of form and without the medium moving bodily with it. Simple examples of waves are to be seen when one end of a taut rope is jerked or when a stone is thrown into a pond and makes ripples on the surface. Waves produced in this way are known as transverse waves, since the disturbances in the medium are perpendicular or transverse to the direction of propagation of the waves. The ripples on water can be seen to travel outwards from the centre of the disturbance, but a cork floating on the surface will execute an up-anddown motion without moving away 52 PRODUCTION AND TRANSMISSION OF SOUND Sec. II
: 5 represents the distance that the motion has travelled during the execution of one com]3lete vibration. Period of a \ ibratioii is the time of one complete vibration, or is the time taken by a particle in travelling from its mean position through the maximum displacement first in one direction and then in the other, finally returning to its mean position. Frequency (n) is the number of vibra- tions in one second. Wave-Train is a succession of waves caused by continuous vibration of the source. DISPLACEMENT OF END A. % Vibration Vi Vibration Ff V* Vibration n 1 Vibration DISTANCE TRAVELLED BY DISTURBANCE IN CORD AB g '/4 Wave-length Vi Wave-length Ti Wave-length 1 Wave-length Fig. 6:7 Proving that V = nl. Velocity (F) is the distance covered in a unit of time (a second). Since during one vibration the disturbance travels I cm. (Fig. 6:7), then during n vibrations, the disturbance travels nl cm. (n wave-lengths). Now, (one wave-length) if n the frequency is vibrations per second, the disturbance travels nl cm. in one second, i.e., the velocity is nl cm. per second. This gives us the wave formula found to be equally useful in all branches of physics. Velocity = frequency X wave-length or V = nl. R I -C.1 R 53 Chap. 6 SOUND audible in all directions, each wave-front, i.e., the leading edge of each wave, must be spherical. How the air responds to the vibrating bell may be illustrated with the aid of the apparatus shown in Fig. 6:10. The Fig. 6:10 Illustrating Longitudinal Wave Motion. steel balls are suspended so that they just touch. When the first one is drawn aside and allowed to hit the ball next in line, none moves except the one at the opIt flies out about as far as posite end. the first was drawn aside. Because steel is elastic, the impact is passed through Such waves (b) Longitudinal Waves Sound waves differ from those described above in that the particles of the medium are displaced from their mean positions backwards and forwards along the line of travel of the wave are known as motion. longitudinal waves, and may be illustrated by reference to Fig. 6:8. There we have a coil spring
stretched between two supports (S, Si). A piece of cloth is tied near its centre. When several coils of the spring are squeezed together a compression, formed. When the coils are released, their elasticity causes them to return to their normal position. The momentum so produced causes them to move past this position, thereby forming a stretched region or rarefaction (R). or condensation (C) is A study of the jerking of the cloth to and fro along the length of the spring will give ample proof of what is happening. It will now be good practice to draw a longitudinal wave-train in a coil spring and label amplitude, particles in the same phase, and one wave-length. Longitudinal waves are always characterized by condensations and rarefactions. Rarefoction Sound Waves from a Vibrating Tuning-fork. the line as a compression wave or condensation followed by an expansion or rarefaction. This is similar to the way in which sound waves are transmitted through air. Ii:6 THE SUPERPOSITION OF WAVES (a) Interference Interesting effects are observed when Fig. Sound waves from a vibrating bell are 6:9. The transverse depicted in vibrations of the gong give rise to condensations and rarefactions alternately, i.e., longitudinal waves. As the sound is 54 PRODUCTION AND TRANSMISSION OF SOUND Sec. II: 6 two waves are simultaneously propagated through the same medium. The resulting displacement at any point of the medium is the algebraic sum of the displacements produced by the two separate waves. When these are in the same direction the effects are thus reinforced, and when In the opposed they are diminished. special case where the two waves are of the same frequency and amplitude, as in Fig. 6:11 (a), each wave will assist the other at all points when die two waves crests and phase, are! troughs of the two waves exactly coinciding throughout the medium. If, however, they are completely out of phase * as in Fig. 6: 11(b) the two waves are i in exact opposition at all points, the crests of one coinciding with the troughs of the other, and accordingly the result- exactly the in I ; j I ing effect in the medium is nil. These phenomena are referred to under the general heading of interference. Special cases of particular interest to us in our study of sound will be presented in Sec. 11:24. (b) Standing
Waves A very important case of interference is seen when two trains of waves of the same frequency and amplitude travel in opposite directions through a medium, for example, original and reflected waves (Chap. 10, Exp. 5). To demonstrate this, attach a light flexible silk cord to one prong of a large tuning-fork. Pass the other end of the cord over a pulley and attach a weight to it. The tuningfork should be activated by an electromagnet to give continuous vibration. In (b) Two Waves In Opposite Phase They Nullify Each Other Fig. 6:11 Production of Standing Waves. 55 Chap. 6 SOUND Vi Period After (a) '/2 Period After (a) Vi Period After (o) ^ Period After (o) A combination of (a) (b) (c) (d) (e) Fig. 6:12 Superposition of Waves. 56 PRODUCTION AND TRANSMISSION OF SOUND Sec. II to place of the tuning-fork an electric bell with gong removed may be used, the cord being tied the clapper, or a special vibrator as shown in Fig. 6:11 (c) may be employed. For reasons to be discussed later, the length of the cord is adjusted until it takes the form shown in the figure. The hazy oval regions where displacement of the cord is greatest are called loops. The points of quiet tlie ends where reflection as well It might be occurs are called nodes. imagined that a loop would occur where the cord meets the vibrator but, in reality, the amplitude of the vibrator is so small compared to that of the cord that it must be considered to be a node. In any case some reflection occurs there, as depends The reason for adjusting the length of to be the cord is rather too difficult explained here. Flowever, this much can be said, that the wave-length of the disturbance tension (caused by the weight) and the frequency of the source. Since each loop is half a wave-length and there must be a whole number of loops in the cord, the length must be adjusted to accommodate a whole number of loops. the on An examination of Fig. 6:12 will help us to understand the phenomenon. The wave composed of dashes is proceeding to the right, the dotted one to the left. They have the same amplitude and wave-length. The solid line is the resultant of the former two. At the start let us assume that the waves are completely out
of phase as in (a). We know that the result will be Onea line of undisturbed particles. quarter of a period later (b), each will have shifted one-quarter wave-length but in opposite directions. -The waves will be in phase now and will reinforce each the resultant other. has wider amplitude than either of the original waves. Diagrams (c), (d), and (e), may be explained as above except For this reason, that the phase is different after each quarter vibration. The combined effect is shown in (f). 4, 8, Examination of the diagrams reveals 10 which are that points 2, 6, one-half a wave-length apart are always at rest and hence constitute the nodes. Points 1, 3, 5, 7, 9 move from rest to a point of maximum displacement on one side then back through the point of rest to a point of maximum displacement on the other and return. These are the loops. Thus standing waves consist of nodes and loops. The distance between successive nodes or is one-half a wave-length. These waves will be useful in understanding vibrations in strings and air columns which will be presented in succeeding chapters. loops 11:7 REFLECTION OF SOUND WAVES Sound waves travelling through the air and striking a smooth hard surface undergo reflection, obeying the same laws of reflection as light waves. That is so can be demonstrated using this the apparatus shown in Fig. 6:13. Sound A B Fig. 6:13 Reflection of Sound. waves from a source S (a watch) are directed by a tube to a hard surface, AB (a drawing-board is suitable for the purpose). A receiver, R (the ear), is 57 Chap. 6 SOUND Canadian National Exhibition Band Shell. Canadian National Exhibition placed at the end of a second tube which, to detect the signals, must be inclined to AB at the same angle as the first In short, the angle of reflection tube. equals the angle of incidence (i). (r) Also, the incident sound (SO), the perpendicular (CO) and the reflected sound The (RO) are in screen CD acts as a shield to protect R from the sound waves transmitted directly from S. the same plane. A very interesting demonstration of the reflection of sound is found in the Museum of Science and Industry at Chicago. Two concave mirrors are arranged a long distance apart. A person standing at the focus of one may whisper softly and the words will be clearly audible to a
person standing at the focus of the other. Echoes are due to reflection. They are produced as the result of a sound 58 PRODUCTION AND TRANSMISSION OF SOUND Sec. II: 8 all etc. will sides, signal directed towards a distant ob(e.g., a wall) being returned to stacle the listener, who thus hears a repetition of the sound a short period after it has been produced. Forests, clifTs, hillreflect sound and cause the formation of echoes. If there are a number of reflecting surfaces at different distances from the source, a series of repetitions of the sound signal, each following the other, will be received. These are known as multiple echoes, and they are heard, for example, when an Alpine horn is blown amidst a number of mountain peaks. The reflection of sounds may have unpleasant results in auditoria that are not properly constructed. The sounds echo and re-echo from the walls so that the effects of one sound have not died The away before the next is made. resulting jumble of sounds is known as reverberation. Further reference of sound will be made in the next section and in section 11:32. reflection to 11:8 THE VELOCITY OF SOUND (a) Methods of Measuring 1. By Direct Measurement The early experiments to determine the velocity of sound in air, made in the late seventeenth and early eighteenth centuries, were based on estimating the difference in time for the light and the of sound to travel to an observer from a cannon fired some distance away (Fig. 6:15). Since the speed of light is very great (186,000 miles per second), the the explosion is seen almost flash instantaneously. Hence the time elapsing between an observer seeing the flash and hearing the report of the explosion may be taken as the time needed for the sound to travel the measured distance between the cannon and observer, and this enables the speed of sound to be calculated. There are two main objections to these simple “flash-bang” experiments. If there is a wind the result will be greater or less than the true value according to whether the wind is blowing from the cannon to the observer or in the opposite direction. The other chief source of error is the “reflex time” of the observer. Thus, if a stop-watch is used in such an experiment there is a difference between the response time in seeing the flash and the starting report and stopping it. This error varies with different observers, and with the
same individual from time to time, and also even with the loudness of the sound. If the cannon is one mile from the obtake about 5 server seconds to travel the distance, and hence a personal error of 1/5 second will introduce an error of four per cent in the the watch, and hearing the sound will final result. 59 Chap. 6 SOUND The accepted values for the velocity of sound in air are tabulated below. It will be noted that for a change of 1 centigrade is a corresponding change in the velocity of sound in air of 2 feet per second or 0.6 metres per second. degree, there Temperature 0°C. 10°C. 20°C. Velocity Ft. per Sec. Velocity Metres PER Sec. 1089 1109 1129 332 338 344 The first accurate determination of the speed of sound was carried out by 1738. Two the French Academy in cannons were used, separated by a distance of about 18 miles to reduce the error due to the “reflex time”. To eliminate the effect of wind, timings were taken (by means of pendulums) in both directions and the average used to calculate the speed of sound. The result obtained was 337 metres per sec. at 6°G., or 332 metres per sec. at 0°C. Later experiments, carried out in the same way, but using chronometers, accurate to one-tenth of a second, gave a mean result of 331 metres per sec. at 0°C. 2. By Echoes If a sound signal is directed to a distant wall or obstacle an echo will be received some time later, the sound wave having travelled twice the distance between the wall and the observer during This suggests a possible the period. method of measuring the velocity of sound. For clear echoes, however, the wall (or reflecting surface) should not be too far distant, and this involves the difficulty of measuring very practical short time-intervals. With a wall 100 yards distant, for example, the echo of a sound signal will be received only about one-half second later. This difficulty has been overcome by using a metronome or 60 an electrically controlled tapper to send out a sequence of sound signals at regular intervals. The distance of the metronome from the wall is adjusted until the echo of one click is heard simultaneously with the next click. The sound signal has clearly travelled to and from the wall during the interval between the clicks. This time-interval is accurately known, and
so the velocity of sound can be It should be noted that since found. the sound signal has to travel back along its track this method automatically eliminates the effect of the wind. Example A metronome was 280 feet from the interval between wall and the time clicks was 1/2 second. Distance covered in 1 /2 sec. was 560 feet In 1/2 sec. sound has travelled 560 feet In 1 sec. sound has travelled 1/2 ‘.. the velocity of sound ^ = 1120 feet per sec. 3. By Resonance In section 11:22, and experiment 10, chapter 10, we shall study resonance experimentally, and shall use the results in the formula V — nl to determine the velocity of sound. (h) Breaking the Sound Barrier In recent years breaking the sound barrier, i.e., flying at the speed of sound (742.5 miles per hour at 0°C.) and more, has become a great test both of the skill of operation and the construction of aircraft. When an advancing craft catches up with its own sound waves a giant barrier of compressed molecules of air must be penetrated, and this requires the power of jet-type engines and an extremely strong construction of the aircraft. This situation PRODUCTION AND TRANSMISSION OF SOUND Sec. II: 9 presents just one of the many practical problems which can only be dealt with because of our modern grasp of the nature of sound. The Velocity of Sound in Various Media Medium Velocity Gases feet per sec. metres per sec. Carbon Dioxide (0°C.) Oxygen (0°C.) Air (0°C.) Hydrogen (0°C.) Liquids Water (9°C.) Sea-Water (9°G.) Solids Brass Oak Glass Iron Aluminum 846 1041 1089 4165 4708 4756 11480 12620 16410 16410 16740 i, 11:9 QUESTIONS 258 317 332 1269.5 1435 1450 3500 3850 5000 5000 5104 A 1. Which of the following statements is correct? (a) All vibrating objects produce sound, (b) All sound is produced by vibrating objects. Explain your answer fully. 2. 3. between (a) Distinguish and longitudinal vibrations. (b) Define: complete vibration, ampli- transverse tude, frequency, period. (a) What is necessary for the transmission of sound? (b) Compard^the transmission of sound through the three
states of matter and suggest a theoretical explanation for any differences. 4. (a) Distinguish between transverse and longitudinal waves. (b) Define: amplitude, wave-length, period, frequency. (c) By what fype of wave-motion is sound transmitted? What are the components of each complete sound wave? 5. 6. (d) What is the fundamental characteristic of wave-motion? Explain fully. (a) Establish the wave formula. (b) Calculate the velocity of sound in air if its frequency is 250 v.p.s. and its wave-length is 4.4 ft. (a) What is meant by the terms "in phase” and "out phase” as applied to any wave-motion? (b) How are standing waves produced? of (c) Define: node, loop. (d) Explain why the distance between two successive nodes is one-half a wave-length. 7. 8. (a) State the laws of reflection of sound waves. (b) Distinguish echoes and reverbera- tions. (a) In what three ways may the velocity of sound be determined? (b) What is the effect of a change of 61 Chap. 6 SOUND 7. At what temperature will the velocity of sound be (a) 1,1 19 ft. per sec. (b) 336 metres per sec.? 8. A thunder-clap is heard 5 seconds after the lightning-flash was seen. How far away was the flash if the temperature of the air were 1 5°C.? 9. When the temperature of the air is 15°C., calculate the wave-length in metric units of the sound from a tuning-fork having a frequency of 256 v.p.s. TO. When the temperature of the air is 25’/2°C., and the wave-lengfh of a sound is 4.40 ft., calculate the frequency of the sound. TT. A signal of 128 v.p.s. has a wavelength of 279. cm. (a) Find the velocity of sound in air. (b) What would be the temperature of the air to the nearest degree centigrade? Express your answer in metric units. T2. The human ear is incapable of disindividual sounds unless they tinguishing are separated by a time interval of at least ]/(q sec. (a) Calculate the length of the shortest auditorium that would
give a distinct echo, (b) What would be the effect if the auditorium were shorter? (Assume that the temperature of the air is 20°C.] T3. A 220 yd. dash over a straight course was timed at 23.2 sec. What would the time have been had the timer started the watch on hearing the sound instead of seeing the flash? (Temperature of air -20°C.) T4. Calculate the minimum speed of an aircraft in miles per hour which has broken sound the air = 5.5°C.) barrier. (Temperature of temperature on the velocity of sound In air? 9. The sound of a gun was heard 1 0 sec. after the flash was seen. If the distance to the gun was 1 1,500 ft., calculate the probable velocity of sound in air. Why is this merely a probable velocity? TO. Two and one-half seconds elapse between shouting across a river 1,375 ft. wide and hearing the opposite bank, (a) Find the velocity of sound, (b) Compare the accuracy of this velocity with that of question 5. from echo the B 1. The horizontal distance between the end points in the swing of a pendulum Is 7.5 cm. What is (a) the amplitude, (b) the distance covered by the bob in one com- plete vibration? 2. The pendulum in question 1 makes 45 complete vibrations in 30 seconds. Calculate the period of vibration. What would amplitude were be the doubled? period the If 3. Calculate the velocity of sound in air if the frequency of sound and its wave1 80 v.p.s. and 6.50 ft., length are (a) (b) 360 v.p.s. and 80.0 cm. respectively. if the 4. Calculate the frequency of a sound and are (a) 1,120 ft. per sec. and 3.50 ft., (b) 340 metres per sec. and 51.0 cm. wave-length velocity 5. What are the wave-lengths of the notes when (a) the frequency is 900 v.p.s. and velocity of sound 1,350 ft. per sec. and (b) the frequency is 625 v.p.s. and velocity of sound is 350 metres per sec.? 6. Calculate the velocity of sound in air in (a) feet per second and (b) metres per second at: 5°C., - 17°
C., 23°C. 62 CHAPTER 7 CHARACTERISTICS OF MUSICAL SOUNDS 11:10 INTRODUCTION (a) How a Musical Sound Differs from a Noise As we have seen, people are quick to classify the sounds they hear, as either musical sounds or noises. Almost everyone finds noises, like the slamming of a door or the rumble of machinery unpleasant, and musical sounds like those or pleasant. of We can establish a more objective difference than this between noise and music. When an oscilloscope is used to compare the sound of machinery and that of a tuning-fork, a trace similar tuning-fork violin a Oscilloscope Tracing of Fig. 7:1 A— Noise B—Musical Sound It is obvious to that in Fig. 7 : 1 results. that the musical sound is caused by rapid regular (periodic) vibrations, while the noise is the result of irregular (non- periodic) vibrations. (b) How Musical Sounds Differ from Each Other If one tuning-fork is struck lightly, and another more vigorously, the second will Sounds that differ emit a louder sound. in loudness differ in intensity. If the sounds from two vibrating tuning-forks with differing frequencies are compared, the fork with the greater frequency emits the “higher” sound. Sounds that differ Further, in “highness” differ in pitch. if the sounds of a vibrating tuning-fork and a vibrating string of the same frequency are compared, there is no difficulty in identifying the origin of each Sounds from different sources sound. may be distinguished because they differ in quality. Thus musical sounds differ from each other in intensity, pitch and quality. It is the purpose of this chapter to study these three characteristics fur- ther. 11:11 THE INTENSITY OF SOUND If a bell that is rung cannot be heard at a distance, we know that we may be able to make it heard by striking it harder. This is so because striking with greater force transfers more energy to the vibrating body, increasing what we call the sounds. This increases the amplitude (energy of vibration) and gives If the sound is it a greater intensity. still inaudible, the other obvious thing that can be done to make it heard is 63 Chap. 7 SOUND the shorten distance between the to It might seem source and the receiver. from this that there are just two factors affecting the intensity of sound, namely amplitude and distance, but the experience of undersea workers in
caissons and diving-bells where the air is under great pressure, is that quite ordinary sounds are unexpectedly loud there. This greater intensity of the sound transmitted results from the fact that increased pressure on a gas crowds the molecules closer and increases the density of the medium. For the same reason, as is well known, sounds transmitted by solids and liquids are louder than when transmitted by air. Thus, a third factor affecting intensity of sound is density of medium. fles, while neighbouring buildings can be protected by double windows. The importance of such efforts to reduce Threshold of Painful Noise Airplane Engine Riveting Machine Heavy Traffic Motor Truck Ordinary Conversation Vacuum Cleaner Average Office Quiet Home, Quiet Conversation Rustle of Leaves Quiet Whisper —;130 —h20 -^110 — 100 -^90 — 80.^ -70\|.( —;60 Q — 50 — 40 -30 — 20 — 10 “0 The particular intensity of sound are: laws governing the Threshold of Hearing 1. The intensity of sound varies directly as the square of the energy of vibration (amplitude) of the source. 2. The intensity of sound varies in- versely as the square of the distance of the receiver from the source. 3. The intensity of sound increases with an increase in the density of the transmitting medium. in vary intensity. (deci — 1/10), The intensity of sound is measured in bels and decibels the decibel being the faintest sound that can be perceived by a normal human ear. Fig. 7:2 shows the amount of noise or “noise level” in decibels in a few common locations, for, like musical sounds, Naturally, noises noises are inevitable wherever there is machinery, but unnecessary discomfort can be avoided by the noise level being measured and steps being taken to eliminate all unnecessary vibration. Noise levels around machinery can be reduced by the use of rubber mountings, mufflers and the like; walls and ceilings can be covered with sound-absorbent wallboard, and air-ducts with sound-absorbent baf- Fig. 7:2 Noise Levels. noise levels is indicated by the fact that temporary or permanent deafness and many other illnesses can result from long proximity to noisy machinery. 11:12 THE PITCH OF SOUND That musical sounds vary in highness or pitch was stated in a previous section. In chap. 10, exp. 6, Savart’s toothed Fig. 7
:3 Savart's Toothed Wheel. wheel ( Fig. 7:3) was used to show what determines pitch. The card held against the teeth of the rapidly rotating wheel received a sequence of taps, and a note, whose pitch increased with the speed of 64 CHARACTERISTICS OF MUSICAL SOUNDS Sec. 11:12 rotation, was heard. If the rate of rotation was doubled, the number of taps per second (the frequency) was doubled. The second note, whose frequency is twice as great, is said to be an octave higher than the first. Thus for a note of high pitch to be sounded, the body must be vibrating rapidly, whereas a slow rate of vibration produces a note of low pitch. In short, the pitch of sound depends on the frequency. The frequency of the sound produced may be determined by applying the formula: frequency of note produced ( v.p.s.) = number of teeth on Savart’s wheel X speed of rotation revolutions per second. in The limits of frequency for notes of are from about 20 to pitch audible 20,000 v.p.s. for the average ear (Fig. 7:4). The range of frequencies used in music is from about 30 to 5,000 v.p.s., the keyboard of a piano extending from 27 to 3,500 v.p.s. A man’s speaking voice embraces frequencies ranging between 100 and 150 v.p.s. approximately. Extreme limits of audibility (for very sensitive ears) may be taken as extending from 20 to 35,000 v.p.s. The lowest notes of a large organ are in the neighbourhood of this lower audible limit, while the squeak of a bat or the noise of a cricket are examples of frequencies in the region of the upper audible limit. Frequencies above this point, referred to as ultrasonic frequencies, are becoming of increasing importance (Sec. 11:33). sounds heard by the human ear wind instruments string instruments frequency limits of human hearing ^ Fig. 7:4 Frequency Limits of the Human Ear. Bell Telephone Company of Canada. 65 Chap. 7 SOUND 11:13 THE DOPPLER EFFECT When a car with its horn sounding approaches a pedestrian at high speed, the pitch of the sound appears to be higher than the true pitch which the driver hears (Fig. 7:5). After the car has passed, the pitch appears to be lower than the true pitch. Similar changes in pitch
occur when the origin is stationary and the observer moves past it. To determine the cause, let us take the case of the origin approaching the In any second, a uniform observer. number of wave-fronts are sent out and they will be a uniform distance apart. However, because the origin is approaching the observer, there will be more than the usual number packed in a given space, i.e,, they will be closer together than before. As a result, more than the normal number will be received by the observer in one second. This will cause an apparent rise in the pitch of the sound. This phenomenon is called the doppler effect. Fig. 7:5 The Doppler Effect. 11:14 THE SONOMETER In stringed instruments, the stretched strings of steel, gut, or silk, are set in a state of transverse vibration by being struck, bowed, or picked as in the piano, violin and guitar respectively. Examination of a piano and violin will reveal that sounds of different pitches are obtained by the use of strings of different lengths, tensions, diameters and densities. To ensure that the sound is loud enough to be distinctly heard, the string is attached to a sounding-box or board. The natural frequency of this is not that of the string but the string will set it in vibration with forced vibrations will increase the volume of the sound. that The laboratory device embodying all these features is the sonometer shown in Fig. 7:6. It consists of a hollow wooden box (A) on which one or more strings (B) are stretched. Permanent (C) and movable (D) bridges and a means of varying the tension (E) are provided. CD AD B C 66 CHARACTERISTICS OF MUSICAL SOUNDS Sec. 11:15 \Ve shall now proceed to use it to study the laws of vibrating strings. 11:15 THE LAWS OF VIBRATING STRINGS (a) The Relationship between Frequency and Letigth After doing experiment 7, chapter 10, results similar to those in the following table are found. Examination of trials 1, 4 and 5 will show that while the frequency of 256 is emitted by 34.4 cm. of string, v.p.s. twice that frequency is produced by onehalf that length and four times the frequency by one-quarter that length. Other possible results would be that three times the frequency is produced by one-third the length, five times the frequency by one-
fifth, and so on. Thus we see, as in column 3 below, that the product of frequency times the length of vibrating string is constant within the limits of experimental error. Therefore, the frequency of the note produced by a vibrating string varies inversely as its length. This is the law of lengths. Results for Law of Lengths Constant Tension — 1000 gm. Length of Wire Producing Unison Frequency of Fork Frequency X Length “ 1. 2. 256 v.p.s. 320 384 512 5. 1024 4. 3. “ “ “ 8806 8832 8832 8806 8806 34.4 cm. 27.6 cm. 23.0 cm. 17.2 cm. 8.6 cm. Example If 30 cm. of wire at a certain tension produces a note with a frequency of 256 v.p.s., what would be the frequency when the length is 40 cm.? Solution 1 The ratio of the new length to the old = — 40 30 the frequency varies inversely as the length. the new frequency is — of the old. 40. the new frequency = 256 X — = 192 v.p.s. 30 40. Solution II the frequency varies inversely as the length, frequency X length is constant. 67 Chap. 7 SOUND the new frequency X the new length old length. the old frequency X the Let the new frequency be x a; X 40 = 30 X 256 ;c = 40 = 192 the new frequency =192 v.p.s. (b) Relationship between Frequency and Tension Adjust the length and tension of a string on a sonometer until it is in unison with a tuning-fork of frequency 256 v.p.s. Keeping a constant length of 25 cm., adjust the weights that stretch the string to get unison with a second, and then again to get unison with a third fork. Record the results as follows, and from them determine the relationship. it After comparing the results of trials 1 and 2, is noted that twice the frequency is caused by four times the tension. A comparison of trials 1 and 3 shows that 4 times the frequency is caused by 16 times the tension. Since the multiplier for the frequency is the square root of the multiplier for the it follows that the frequency tension, of the note emitted by a vibrating string varies directly as the square root of the tension. This is the law of tensions. Frequency of Fork 1. 128 v.p.s. 2. 256 v.
p.s. 3. 512 v.p.s. Tension 385 gm. 1540 gm. 6160 gm. Example A string with tension of 2000 gm. produces a note with a frequency of 300 v.p.s. What would be the frequency of the note if the tension were 4500 gm.? Ratio of the new tension to the old = 4500 9, = 4 2000 ’. the frequency varies directly as the square root of the tension. the new frequency will be the new frequency = 300 X 4500 of the old 2000 ^ = 300 X - = 450 v.p.s. 4 2 (c) Relationship between Frequency and Diameter (d) Relationship between Frequency and Density By an experiment somewhat analagous to (a) we may determine the law of diameters, i.e., the frequency of the note emitted by a vibrating string varies inversely as the diameter. frequency of The law of densities states that the the note emitted by a vibrating string varies inversely as the square root of the density of the material. All four laws may be illustrated by 68 CHARACTERISTICS OF MUSICAL SOUNDS Sec. II; 16 the tuned, examination of a violin. To increase the frequency of a note, the violinist shortens the string with his finger. When a violin tension to is increase the frequency and decreased to It will also be decrease the frequency. noted that those strings with greatest densities and diameters the lowest notes. increased produce is 11:16 HOW A STRETCHED STRING VIBRATES We have just considered the simplest mode of vibration of a stretched string wherein the string vibrates as a whole. There is a loop in the centre with a node at each end (Sec. 11:6). When vibrating thus, the string is emitting the note of lowest frequency, the fundamental. However, the in other ways to produce notes of higher frequency (Chap. 10, Exp. 8). string may vibrate When the string vibrates in halves, the note produced has twice the frequency of the fundamental and one-half the wave-length. This is the first over- wave-lengths tone or.second harmonic. When vibratthirds, quarters and fifths, the ing in frequencies produced are three, four and five times that of the fundamental, and onethe are quarter and one-fifth of the fundamental. The notes are called the second overtone or third harmonic and so
on. Fig. 7 : 7 shows some modes of vibration of a stretched string. one-third, fundamental when that We see that a string may vibrate in parts, and as a whole as well. When it is vibrating in parts, the frequency of the note is a multiple of that of the fundamental and the notes are called the harmonics or overtones of the string. Frequently these overtones accompany the is sounded, and give quality to the sound Very produced (Chap. 10, Exp. 9). few sources, on the other hand, produce the fundamental free of overtones. The tuning-fork is one that does, but even in it the overtones are present at the bevibration, vanishing as ginning of its It is this absence of overtime goes on. note FREQUENCY WAVE-LENGTH n I Fundamenfal l\ & First Overtone A\ N A\ N N Second Overtone N A\ A\ A\ N N N N Third Overtone N N 2N 3N 4N Fig. 7:7 Nodes and Loops in a Vibrating String. 'A I 'A I 'A I 69 Chap. 7 SOUND 8 Fig. 7:8 Oscilloscope Tracings of Tuning Forks Sounded (a) Singly A—Tuning-fork B—Organ Pipe (b) Pairs tones that makes the tuning-fork valuable in the study of sound, though at the same time it makes the note dull and uninteresting, for it is the overtones that make a note rich and interesting to the listener. 11:17 QUALITY OF SOUND If respectively. Let us analyse the vibration of a fundamental and its harmonics by means of a cathode-ray oscilloscope. the fundamental has a frequency of 128, the first two overtones have frequencies of 256 and 384, shows the results of sounding tuningforks of these frequencies singly and in groups. When sounded singly, we see differences in frequency and wave-length of the notes. When sounded in groups, we see complicated wave forms which represent the blending of the fundamental and one or more overtones. Fig. 7 : Next, with the aid of an oscilloscope, let us analyse notes from a tuning-fork and several other different sources having the same fundamental frequency. Fig. 7:9 shows several traces made in such a way. The regular trace of the is emitting tuning-fork indicates that it but a single tone.
The complicated wave forms of the others indicate that: D—Violin Fig. 7:9 Oscilloscope Tracings. 70 CHARACTERISTICS OF MUSICAL SOUNDS Sec. II : 18 1. They contain tones (overtones) in addition to the fundamental. 2. That some have more of these over- tones than others. 3. That in some, the overtones are more prominent than in others, We may conclude therefore that the quality of a musical note is dependent on the number and relative prominence of the overtones that occur along with the fundamental. is the quality of It the sound that enables us to distinguish notes of the same pitch and intensity from different sources. 7. QUESTIONS II : 18 1. A between (a) Distinguish sound and a noise. (b) What are the three distinguishing characteristics of musical sounds? musical a 2. (a) Define intensity of sound. (b) State three factors that affect the intensity of sound. Illustrate each with a suitable example. 3. (a) Define pitch. (b) Describe an experiment to illustrate upon what the pitch of sound depends. (c) Make up a set of observations and show how the frequency of a given note may be calculated. 4. (a) Describe the sound of a train whistle as the train moves rapidly away from you. (b) Explain this phenomenon fully. 5. Describe a sonometer and state the purpose of each of its parts. 6. (a) State four factors that affect the frequency of a vibrating string. the Law of Lengths. A (b) State stretched string 50 cm. long vibrates with a frequency of 1 50 v.p.s. What will be its frequency when the length Is (i) 10 cm., (ii) 75 cm.? (c) State the Law of Tensions. A stretched length vibrates with a frequency of 1 25 v.p.s. when its tension is 900 gm. What will be its frequency when the fixed string of tension is (i) increased to 2500 gm. (ii) decreased to 144 gm.? (a) Describe an experiment to show the modes of vibration of vibrating strings. (b) Define; fundamental, overtone. (c) What governs the quality of a note? B 1. A certain note has a frequency of the frequencies 480 v.p.s. (a) Determine of notes that are one
, two, and four octaves above the given note. (b) Find the frequencies of notes that are one, three and five octaves below the note. 2. A toothed wheel with 40 teeth Is rotated at the rate of 360 revolutions per minute while a card is in contact with the teeth. Calculate the frequency of the note heard. 3. A toothed wheel having 66 teeth is rotated while in contact with a card. What will be the speed of rotation in revolutions per minute when the frequency of the note produced Is 352 v.p.s.? 4. How many teeth Savart’s wheel have if the speed of rotation is 540 revolutions per minute and the frequency of the note produced Is 1 350 v.p.s.? will a 5. Savart’s toothed wheels generally are arranged in sets of four on a common shaft with 12, 15, 18, 24 teeth respectively. 71 Chap. 7 SOUND. frequency of 540 v.p.s. What would be the weight the became 16000 gm., 1000 gm.? frequency stretching If 10 A piano string is 60.0 in. long. It vibrates at 260 v.p.s. A piano tuner changes the tension from 25.0 lb. to 36.0 lb. What will be the new frequency? n. A string 40.0 cm. long and having a tension of 1 600 gm. emits a note of frequency 1 28 v.p.s. Determine the tension of this string when it vibrates with a frequency of: 64 v.p.s., 1 60 v.p.s. 12. A string 36.0 in. long under a tension of 1 6.0 lb. vibrates with a frequency of 256 v.p.s. What is the vibration frequency if the length is increased to 54.0 in. and the tension is increased to 81.0 lb.? long 13. A string 100 cm. under a tension of 4900 gm. has a frequency of 280 v.p.s. What is the frequency if the 1 25 cm. and the length is increased to tension reduced to 2500 gm.? When rotating at the average rate of 21 Vz revolutions per second, they produce frequencies corresponding to C major chord at middle C on the piano, i.e., CEGC'. Determine the frequency of each note in the chord. 6. A stretched string 45.0 cm. long emits a note
with a frequency of 300 v.p.s. What would be the frequency if length became 15.0 cm., 60.0 cm., 20.0 cm.? the 7. The A string of a violin vibrates at 440 v.p.s. The string is 40.0 cm. long from If the violinist moves his bridge to nut. finger so that only 30.0 cm. of the string vibrates, what will be the frequency of vibration? 8. A certain vibrating string 50.0 cm. long emits a note with a frequency of 320 v.p.s. Whaf length of string would vibrate with the following frequencies: 640 v.p.s., 200 v.p.s., 457 v.p.s.? 9. A string 30.0 cm. long stretched by a weight of 4000 gm. emits a note having a 72 CHAPTER 8 RESONANCE AND INTERFERENCE PHENOMENA I I, I! 11:19 THE MEANING OF RESONANCE As resonance is a new idea, we shall find out what it means using the apparatus shown in Fig. 8:1. This consists of several pendulums attached to a cord tied between two supports. When one is vibrated transversely, the motion will be transmitted the supporting cord. Any other pendulum through the rest to Fig. 8:1 Mechanical Illustration of Resonance. will vibrate erratically, starting, stopping, but never accomplishing the persistence of vibration referred to above. Now, when impulses from one body affect another having the same period of vibration, the second will begin to vibrate with increasing amplitude. If it is already in motion, the amplitude will become greatThis effect is known as resonance er. and will be very valuable in explaining the phenomena that follow. 11:20 RESONANCE IN AIR COLUMNS That air columns can be set in vibration and made to produce sounds of a definite pitch is well illustrated by such simple experiments as blowing across empty test-tubes of various lengths. Such air columns have a natural period of vibration depending on their length. If the fluctuations of pressure at the end of the column (caused by blowing) have the same period as that of the air column, resonance will occur. The column will be in a state of violent sympathetic vibration, and a strong note will be heard. In our study of air columns, we shall use tubes of uniform cross-section. If the tube is closed at one end, it
is called a closed tube, while if it is open at both ends it is designated an open tube. of the same length and period of vibration will take up the vibratory motion and move with increasing amplitude. The others that have different periods (a) The Closed Tube After performing the experiment to demonstrate resonance in a closed tube (Chap. 10, Exp. 10), let us consider 73 Chap. 8 SOUND what occurred. When the sound that proceeds down the tube is reflected at the closed end the wave returns without change of phase. Thus a condensa- Condensation goes down and is reflected up. li Wave-length Fig. 8:2 Closed Tube in Resonance with Tuning-fork. phase occurs tion is reflected as a condensation and a rarefaction as a rarefaction. As the sound arrives at the open end a change as follows : when a in rarefaction reaches the open end some air is taken into the tube, and a condensation goes down the tube; when a condensation reaches the open end some air spills out of the tube and a rarefaction goes down the tube. Thus a condensation returns as a rarefaction, and a rarefaction as a condensation from the open end. half vibration, diagram (b), a rarefaction will go into the tube which tends to reinforce the rarefaction already proceeding downward. This process continues until the air in the tube is vibrating with such wide amplitude that it becomes the major source of the sound heard. It should be apparent that the sound travelled twice the length of the closed tube during one-half vibration, and therefore the length of the closed tube is equal to one-quarter of the wave-length. (b) The Open Tube Open tubes will also vibrate in resonance with sources of sound such as It has been found that tuning-forks. during one vibration the sound travels twice the length of the tube, and therefore the length of the open tube is equal to one-half of the wave-length. It will be evident, therefore, that the open tube that vibrates in resonance with a tuningfork of a certain frequency is twice the length of the closed tube. Closed Tubes Open Tubes in resonance with it. Fig. 8:2 shows a vibrating tuningfork held over a closed air column which For greater is simplicity we shall confine our attention to the movements of the lower prong, since movements of the upper one do not alter the final result. As the prong
of the tuning-fork traces one-half a vibration, diagram (a), a condensation is sent down the tube and is reflected at the closed end as a condensation. When it reaches the open end it will be reflected down the tube as a rarefaction while the air that spills out forms a condensation the condensation pro- that duced above the prong of the fork. the length of the tube is such that the fork is about to execute the next one- reinforces If 74 Fig. 8:3 Modes of Vibration in Air Columns. 11:21 MODES OF VIBRATION IN CLOSED AND OPEN TUBES In vibrating air columns (Fig. 8:3), there will be nodes and loops ( Sec. 11:6). In the closed tube there will be RESONANCE AND INTERFERENCE PHENOMENA Sec. 11:22 a node at the closed end and a loop at the open end. The length of closed tube will be one-quarter of a wave-length when it is responding to its fundamental For the overtones, the distance tone. from node to loop must also be onequarter of a wave-length. After examination of the diagram, it will be evident that the closed tube can be in overtones whose resonance the frequencies are odd-number multiples of that of the fundamental. with In the open tube there will be a loop at the open ends and a node will occur in the middle when in resonance with the fundamental. The length of the tube will be one-half a wave-length. For overtones, the tube must be capable of containing several half wave-lengths. Figure 8:3 shows how this can be done and makes it clear that the open tube can be in resonance with all the over- tones. I I j [ V I II : 22 DETERMINING THE VELOCITY OF SOUND IN AIR BY RESONANCE IN AIR COLUMNS (a) Closed Tubes As explained in section II: 20(a), the condensation travelled twice the length of the tube during one-half a vibration of the prong of the tuning-fork. Hence, sound must travel four times the length of the tube during one vibration of the prong. Since the distance energy travels during one vibration is one wave-length, the wave-length of sound must be four times the length of the closed tube which is in resonance with the tuning-fork. In the true wave-length actual
practice, must be augmented by.3 times the diameter of the tube (see note) but for purposes we may disregard our Therefore, wave-length (/) of sound = 4 X length of closed tube (L) giving resonance. it. Example A tuning-fork whose vibration frequency is 256 v.p.s. produces resonance with a closed tube 13.0 inches long. Calculate the velocity of sound in air.? n = 256 v.p.s. l:=4L = 4x222. 12 ft. (Sec. 11:5) T = 256 X =1109 4 X 13.0 12.'. Velocity =1109 feet per second Since the measurements are accurate to three significant digits, the proper answer is 1 1 1 X 10 feet per second ( Sec. 1:3). What would be the approximate temperature of the air in the above example? (b) Open Tubes In section II: 20(b) ; it was stated that sound travels twice the length of the open tube during one vibration. There- fore, the wave-length (/) of sound = 2 X the length of the open tube (L) (see note), A tuning-fork whose vibration frequency is 1024 v.p.s. produces resonance with a tube 17.2 cm. long. Calculate the velocity of sound in air. Example 75 Chap. 8 SOUND V=? n = 1024 v.p.s. l = 2L = 2 X 17.2 cm. \'V^nl V = 1024 X 2 X 17.2 100 = 352.3 Velocity = 352.3 metres per second or 352 metres per second. What would be the approximate temperature of the air in the above example? Note In very accurate work a correction must be made for the change in pressure influencing the sound waves a short distance from the end of the tube. In a first course in physics, however, this factor need not be considered. For closed tubes, the end correction of.3 X the diameter of the tube must be added. For open tubes, you make the same correction for each end. The phenomenon is caused by the inertia of the air molecules. 11:23 SYMPATHETIC VIBRATIONS Two tuning-forks frequencies are mounted on hollow wooden boxes each open at one end (Fig. 8:4). identical of Fig. 8:4 Identical Tuning-forks to Illustrate Sympathetic Vibrations. The size of the air
column is such that its natural period of vibration is the same as that of the fork. The boxes are placed a short distance apart with their open ends facing each other. When one fork is vibrated and then silenced shortly afterwards, a sound of the same pitch is still heard (Chap. 10, Exp. 11.) It is found to originate from the other fork. This response of one body to the sound 76 waves caused by the vibrations of another is called sympathetic vibrations. When a piece of plasticine is attached to the prongs of one fork its frequency is alIf the above experiment were tered. repeated this fork would not set up vibrations in the other. This shows that the two forks must have identical periods for sympathetic vibrations to occur. Vibrations from the fork cause forced vibrations in the box and in turn the air in the box vibrates in resonance with them. The vibrations pass through the air to the other box, through the same sequence of events as above, but in reverse order, causing the second fork to vibrate. 11:24 INTERFERENCE OF SOUND WAVES (a) Silent Points around a Tuning-Fork When a vibrating tuning-fork is held vertically and rotated near the ear alternate loud and faint sounds will be It will be heard (Chap. 10, Exp. 12). found that the faint sounds are obtained when the tuning-fork is held cornerwise to the ear. To understand this phenomenon, we should recall that in transverse RESONANCE AND INTERFERENCE PHENOMENA Sec. 11:24 vibration the prongs of the fork move together for half a vibration and apart for the next half. When they approach a compression each other (Fig. 8:5) R. tube (Chap. 10, Exp. 13). It consists of two U-shaped tubes that telescope in and out of each other (Fig. 8:6). One side has a speaking-tube, the other an listen. When a opening at which to sound is sent in and the length of the two paths is adjusted, faint sounds are heard in some positions and loud ones at If the two paths that the sound others. follows differ by one-half a wave-length, or an odd number of half wave-lengths, the two parts of the sound will arrive out of phase at the observer and a faint If the two paths sound will be heard. are equal, or differ by a whole number of wave-lengths, the two parts of the I
j rarefaction (Ri) at either side. These r two waves spread out in all directions and, because they are in opposite phase, interfere with each other, producing silence when they meet at the corners (S). It is often noticed that the intensity of sound varies in different parts of an auditorium without any obvious cause. One possible reason for this is the interference of direct waves with reflected If these are out of phase they will produce a faint i sound as happened at the corners of the 1 waves from walls and ceiling. I I tuning-fork above. Another cause is discussed in Sec. 11:30. (b) The Herschel Divided Tube Fig. 8:6 The Herschel Divided Tube. I be can produced Interference by dividing a wave disturbance into two parts, conducting each along a separate path, and then blending the two. This'can be accomplished by the Herschel sound will arrive in phase at the observer and a loud sound will be heard. This phenomenon is used to find the wavelength of sound. If the frequency of the 77 Chap. 8 SOUND note is known, the velocity of sound can be calculated. (c) Beats If the prongs of one of two middle C tuning-forks are loaded with plasticine, the frequency of its vibration will be slightly lower than that of the other. If these forks are sounded together, a sound will be heard which periodically increases and decreases in intensity. The alterations in the loudness of the sound are called beats. Consider each of the waves sent out by the forks as transverse waves. By representing one with a solid line and the other by a dotted line, as in Fig. 8:7 (a), we see that they become progressively more out of step until one cancels the other. If the lines are continued they will eventually arrive in step, although one will be a wave-length in front of the other. Now, when waves are out of phase they interfere with each other with consequent reduction in amplitude of vibration or loudness of the sound. When completely out of phase will be no movement and no there sound. When completely in phase, there will be a greater amplitude and a louder sound. cases there will be a gradual increase or de- Between these extreme 78 RESONANCE AND INTERFERENCE PHENOMENA Sec. 11:25 crease in both amplitude and loudness. 8: 7(b) shows the result of such Fig. : interference. i I i I j j Fig. easily
. 8; 7(c) Flaving studied beats with reference to transverse waves, we may understand their production in sound waves more shows two sound, waves of slightly different frequencies being produced simultaneously. Assuming that they begin in phase, two condensations or rarefactions will occur together, producing a loud sound or a beat. As 1 the two waves get out of phase, the sound will become fainter and the more out of phase they are, the fainter the be. When completely out of phase, as when a condensation from i one and a rarefaction from the other'occur together, silence results. As they ‘ become progressively more in phase, the a! maximum, at which point a loud sound'sound will increases intensity reaches until it I'or beat will occur as before. A repetition of this sequence of events gives us noticed when two tuningforks of slightly different frequencies are effect the vibrated together. If the forks being used had a difference in frequency of one v.p.s., one beat per second would result. Similarly, a difference of two v.p.s. would produce two beats per second and so on. In general, the number of beats per second equals the difference between the frequencies of the two notes. This provides a convenient means of determining the frequency of a sound. (How could Moreover, musical inthis be done?) struments are tuned by listening for beats. The fewer the beats, the more nearly alike are the two frequencies. When unison is achieved, no beats may be discerned II : 25 QUESTIONS (a) What is meant by resonance? fully. 5. (a) How are beats produced? Explain (b) Explain resonance in closed tubes. 2. (a) A closed tube 1 2 in. long is in resonance with a tuning-fork whose is 300 v.p.s. vibration frequency Calculate (i) the wave-length of the sound (ii) the velocity of the sound in air. (b) What would be the length of a tube open at both ends that would be in resonance with the tuning-fork used in part (a)? (b) What determines the number of beats per second? 6. A person holds down the "loud pedal” of a piano and sings a note. Account for the humming sound heard. Why does more than one string respond? 7. Account for the sound produced by blowing across the top of an empty testtube. What would be the wave
-length of such a note? 3. Explain and give examples of sym- pathetic vibrations. 8. Account for the rise in the pitch of sound heard as a cylinder is gradually 4. (a) What is the cause of interference in sound? (b) Explain (i) silent points around a tuning-fork, (ii) variations in the loud- ness of sound as Herschel’s divided tube is elongated. filled with water. 9. Explain why a wavy sound is frequently heard when a tuning-fork mounted on a sounding-box, the open end of which faces a wall, is moved towards and away from the wall. Try it. 79 Chap. 8 SOUND B 1. (a) Calculate the wave-length of a note that gives resonance with (i) a closed tube 15 in. long, (ii) an open tube 6 In. long. (Disregard the cor- rection for diameter.) 5. A closed tube 4.0 ft. long responds to a frequency of 70 v.p.s. Find the temperature of the air. 6. A closed tube 40.0 cm. long responds the to a frequency of 220 v.p.s. temperature of the air. Find 7. A resonance box is to be made for (n = 440 v.p.s.). When the a tuning-fork velocity of sound in air is 330 metres per second, what would be the shortest length of box, closed at one end, that would resonate with it? 8. Two forks, having frequencies of 384 and 380 v.p.s. respectively, are sounded together. How many beats per second will be produced? 9. When a tuning-fork (n — 4S0 v.p.s.) is sounded with another of slightly different pitch and there are 6 beats per second, what are the possible frequencies of the second fork? How would you determine whether its frequency would be higher or lower than the other? (b) Determine the velocity of sound (n = 220 results shown in tuning-fork gives v.p.s.) the air a in if question 1 (a). 2. Compare the frequencies to which a closed tube 1 2 in. long and an open tube of the same length will respond, the temperature of the air being 1 91/2° C. 3. Find the frequency of a note that resonates with a closed tube 1 0.5 in. long, the temperature of the air being
'\5Vi°Q. 4. Find the length of closed tube that will respond to a frequency of 288 v.p.s., the temperature of the air being 25V2°C. Express the answer in both British and metric units. 80 CHAPTER 9 APPLICATIONS OF SOUND ing between these membranes sets them in vibration in a way similar to blowing between the strands of a stretched elastic band. The faster the air moves, the the intensity of the sound greater is produced. The particular quality of the sound depends on resonance in the cavities of the mouth (m) and (n). Variaare caused by muscles altering tions the size and shape of these cavities. In the mouth, the tongue measure, makes the major changes. large (t), in 11:27 THE EAR The ear is the most wonderful sound It con- receiver that can be imagined. the outer ear, the sists of three parts: middle ear, and the inner ear. Sounds are collected by the pinna (Fig. 9:2) and directed into the ear canal to the eardrum. The ear-drum consists of a thin (3/1000 inch thick) tightly stretched membrane that is set in vibration by the sound waves and serves as the gateway to the middle ear. the ear there Within middle are three bones named because of their shape, the hammer, the anvil and the stirrup. The hammer is in contact with the eardrum, the stirrup with the oval window leading to the inner ear, and the anvil connects the two so that the vibrations of the ear-drum are transmitted to the inner ear. The middle ear is joined to the throat by the eustachian tube, the purpose of which is to equalize the air pressure on either side of the ear-drum. ^! j I! : 26 THE VOICE Of all sources of sound the voice is the most wonderful. The vocal cords in the larynx (Fig. 9:1) are two (c) elastic membranes whose thickness, length and tension affect the pitch in response to the will of the person and in keeping with the maturity and sex of the individual. Air (a) from die lungs (1) pass- Chap. 9 SOUND This adjustment of pressure can be felt when motoring in hilly country. The inner ear contains a spirallyshaped organ, the cochlea, containing a fluid which is agitated when the oval window vibrates. Movement in this fluid will
cause hair-like projections to vibrate, transmitting small nerve impulses through the auditory nerve to the brain. In addition to the cochlea, the inner ear contains another organ known as the semicircular canals, which is associated with posture and balance. 11:28 MUSICAL SCALES The story of the evolution of the existing musical scale is a long and interesting one. The scale which gives maximum pleasure to us is one in which the frequencies of the notes are in the simple ratios shown (page 83). This scale is known as the diatonic scale, which on the tonic sol-fa corresponds to the notes doh, ray, me, fah, soh, lah, te, doh, or more familiarly perhaps, C, D, E, F, G, A, B, C'. The first note on the scale is called the tonic, and the last note, of twice the frequency of the first, the octave. The number of the note (counting from the tonic) defines a musical interval on the scale; thus the interval from C to D is a second, that from C to E a third, and so on. These intervals correspond respectively to frequency ratios of 9/D _ 288\ 8\C ~ 256/’ 4\C ~ 256 / 5/E _ The last row of figures gives the ratios 82 6 APPLICATIONS OF SOUND Sec. 11:28 The Diatonic Scale No. of note Notation Absolute frequencies (scientific pitch)* Frequency ratios 2 D 1 3 4 C 256 288 320 341.3 384 426.6 480 512 C 15 8 Interval ratios 9 8 10 9 16 15 9 8 10 9 9 8 16 15 *In science C represents a frequency of 256 v.p.s. but for concert work however, C is usually tuned to 261 v.p.s. I of the frequencies between successive These are known notes on the scale. as the interval ratios, of which it will be seen that there are three. These are 9 / 0 8VC ^ and 288 \ = — ), — ( — 10/E _320 9\D "~288 256/ 16/F 15\E ~ 341.3\ 320 } 1 etc. A note is sharpened when raised by an interval of 25 - e.g., Clt = — X 256 = 266.7 v.p.s. 25 24 24 A note is flattened when lowered by an interval of 24 —,
this scale and difficulties of modulation are overcome. It should be noted that a small amount of discord is inevitably present in instruments of fixed pitch, such as the piano and organ, which are tuned according to this scale. Thus reference to the tables will show that a chord of the three notes C, E, G, which is known as a major triad, does not have exactly the desired frequency ratio 4: 5: 6 as on the diatonic scale. However, in spite of this imperfection, this scale meets all the requirements admir- ably. 84 Photo by Everett Roseborou^h Ltd, APPLICATIONS OF SOUND Sec. 11:29 11:29 MUSICAL INSTRUMENTS (a) Stringed Instruments (Fig. 9:4). extensive list of these The reader will be able to suggest an All! hav'e a sounding-box or board over which one or more strings are stretched. This is made to vibrate at the same frequency as the vibrating strings to give greater'intensity of sound. The frequencies of the notes emitted by the strings are de, termined by their lengths, tensions, diameters, and densities. Some instruments, : e.g., the banjo-like group, have a fretboard to which the string is pressed, thus pre-determining the length required for a certain note. Those of the violin group have no frets and the performer : must rely on his ear to obtain the desired I note when he presses and vibrates the string. In the piano, there is a string of tension and All stringed in-!' density for each note. diameter, certain length, I j I j j struments produce notes with one or more overtones, their number depending on the manner of vibrating the string and the place where it is bowed, picked, or struck. (b) Wind Instruments These include the pipe and reed organs, the wood-winds and the brass instruments (Fig. 9:5). They involve a means of vibrating a resonant air column either of the open or closed variety. In some the air column is of fixed length and in others it may be varied by means of valves or a sliding telescoping device. The closed pipe or flute type of pipe of an organ is pictured in Fig. 9: 6(a). Compressed air (A) enters the space (C), is forced through the slit (S) and, on striking the lip (L), causes
periodic variations in pressure. The length of the pipe is adjusted so that it resonates with these and gives out a musical tone, including overtones. Being a closed pipe. Cello Violin Guitar Harp Turner Musical Instruments Lyon Healy, Chicago. Fig. 9:4 Stringed Instruments. Chap. 9 SOUND Fig. 9:5 Wind Instruments. Greene Music Co. Gtd it has a node at the closed end and a loop at the open end and the sound contains the overtones whose frequencies are oddnumbered multiples of the fundamental. Owing to the greater number of higher overtones pipes, organs generally contain that kind, but they have the disadvantage of being twice as long for a given note. obtained open with An organ pipe of the reed-type is pictured in Fig. 9: 6(b). Here air (A) a metal-covered chamber (C) enters containing the stem of the pipe (S) with the reed (R). The note is determined by the reed and the air column serves resonance and improve the give to quality of the note. Instruments such as the flute and piccolo are like the flute-type of organ pipe. Different notes are made by opening holes along the length of the air column. The saxophone, bassoon, clarinet, and oboe use a reed to set the air column in vibration, and the pitch is varied by opening and closing holes to vary the length of this column. In brass instru- 86 ments the lips of the performer act as a double reed. Differences in pitch are produced by changing the length of air column with “valves” as in the cornet and similar instruments. complished by telescopic sliding U-shaped part of the tube in or out as in the trombone, or by over-blowing to produce the overtones as in the bugle. This is the ac- All musical instruments require frequent tuning due to mechanical defects or changes in temperature. Temperature affects not only the lengths of the strings in stringed instruments but the frequency of a resonant air column. The latter may be understood when we recall that the velocity of sound in air changes with the temperature. Since V — nl and I is constant, then changes in V cause a corresponding change in n. (c) Drums There are several types of drums used in bands and orchestras (Fig. 9:7). The bass and snare drums and the tympani They may
use ultrasonic vibrations, best i.e., having frequencies above the audible These can be beamed and on range. being detected are of such a nature as not to be confused with other vibrations in the water. 11:33 THE FUTURE OF SOUND the No one can foresee future of sound. The properties of sounds in the audible range, that is, 20-20,000 v.p.s., are well understood. However, there is much to be learned about the ultrasonic vibrations whose frequencies are from 20,000 to 500,000,000 v.p.s. The dog whistle (20,000 v.p.s.) and the squeak of a bat (30,000 v.p.s.) are at the lower limit of this group of vibrations. sea was used at Some present uses for ultrasonic vibrations follow. When used at an intensity of 160 decibels or more they have been used to remove the dust and soot from chimney gases. During World War II Sonar (Sound, Navigation, and Rangfor sounding, ing) locating submarines or other ships, and for underwater communication. Peacetime underwater uses include locating schools of fish and sunken ships. Another use is to cause molten metals to set more thus giving them finer grain quickly, structure and, thereby, greater strength. Conversely, it is used by large organizastructural tions materials such as concrete. Still another is in homogenizing milk. The physiological these high-frequency sound waves are only Research beginning to be understood. IS proceeding on measuring the body’s a view to tolerance deriving possible curative values. Truly, the future of sound may be amazing! discover them, effects flaws with of to to in Sea Bed Fig. 9:14 Determining the Depth of the Sea. By means of a timingunder water. device the interval may be determined. This must be halved when finding the depth of the sea. (Why?) Knowing the velocity of sound in water and the time, the depth can be determined. The hydrophone is a special receiver for underwater work designed to respond to vibrations from one direction only In time of war, it serves a useful purpose in locating enemy submarines. 92 APPLICATIONS OF SOUND Sec. 11:34 QUESTIONS II : 34 1. 2. A (a) Describe the larynx. (b) How do we produce sound in the larynx? (c) Give varying reasons the for quality of different
voices. (a) What are the three main divisions of the ear? Name the parts and purpose of each. (b) Describe how we hear. 3. (a) Define: tonic, octave, major tone, minor tone, semitone, major triad. (b) Distinguish between diatonic scale, and scale of equal temperament or chromatic scale. orchestra under the headings: (a) stringed (b) wood-wind (c) brass Give at least three examples of each. percussion. (d) 5. Describe how the acoustics of lecture halls may be improved. 6. Describe several ways of recording sounds. 7. In sounding a lake, the time lapse between producing a sound and hearing the echo is 0.75 sec. The velocity of sound in water is 4750 ft. per sec. Calculate the depth of the lake at that point. 8. (a) Distinguish ultrasonic and supersonic. between the terms (b) Give several uses for ultrasonic 4. Classify the instruments of a school vibrations. 93 CHAPTER 10 EXPERIMENTS ON SOUND EXPERIMENT 1 To study transverse vibrations. (Ref. Sec. II;3)j Apparatus A simple pendulum and support, stop-watch Fig. 10:1 Method 1. Attach the pendulum to the support. Draw the bob aside and let it swing freely. 2. With the bob at rest, mark its position by a chalk mark on the table. Draw the bob aside and measure the distance it travels to either side of the rest position. 3. While the bob is swinging measure the time required for 30 complete vibrations. Calculate (a) the number of vibrations per second and (b) the time required for one vibration. 4. Repeat part 3 using a greater and a smaller amplitude. 5. Repeat pai't 3 with a longer and a shorter pendulum. Observations 1. (a) In the simple pendulum, what is the direction of motion relative to the length of the vibrating object? (b) What is one complete vibration? 94 2. 3. EXPERIMENTS ON SOUND How do the distances that the bob swings to either side of the rest position compare in magnitude? Time for 30 VIBRATIONS The number OF VIBRATIONS PER SEC. The time for 1 VIBRATION The given pendulum The same with greater amplitude The same with smaller
amplitude The pendulum made shorter The pendulum made longer Conclusions 1. (a) What type of vibratory motion is illustrated by the pendulum? (b) Define complete vibration. 2. Define amplitude of vibration. 3. Define (a) frequency of vibration, (b) period of vibration. 4. What efTect has changing the amplitude on the frequency and period of vibration? 5. What effect has changing the length of the pendulum on its fre- quency and period? Questions 1. Why do we call these vibrations transverse? 2. What changes take place in amplitude as the body is allowed to vibrate for a long time? What effect has this on the period or frequency of vibration? 3. Why is the period not dependent on the amplitude? 4. Why is the pendulum a suitable device for controlling a clock? EXPERIMENT 2 To study longitudinal vibrations, (Ref. Sec. 11:3) Apparatus A coil spring, weight, support, stop-watch. Method 1. Suspend the weight from the support by the coil spring. Draw the bob down and release it. Fig. 10:2 95 Chap. 10 SOUND 2. When the weight is at rest, mark its position by a chalk mark on some vertical object such as a ruler. Draw the weight down and note the distance that it travels above and below the rest position. 3. While the weight is moving measure the time required for 30 complete vibrations. Calculate (a) the number of vibrations per second and (b) the time required for one vibration. Observations 1. (a) In the coil spring what is the direction of motion relative to the length of the vibrating object? (b) What is one complete vibration? 2. How do the distances that the weight moves to either side of the rest position compare in magnitude? 3. (a) What is the number of vibrations in 30 seconds? (b) What is the number of vibrations in one second? (c) What is the length of time for one vibration? Conclusion 1. What type of vibratory motion is illustrated by the coil spring? 2. Give the meaning of the terms complete vibration, amplitude, fre- quency and period. Questions 1. Why do we describe these vibrations as longitudinal? 2. What would be the mode of vibration of a tuning-fork at a, b, c, d? Test your answers by exploring the fork with a pith ball. a b c
d EXPERIMENT 3 To determine whether or not sound requires a material medium for its transmission, (Ref. Sec. II: 4) Apparatus Bell-in-vacuo (Fig. 6:5), exhaust pump, wax or vaseline, electric wires, two dry cells, switch. Method 1. Seal the bell-in-vacuo onto the pump plate with the wax and connect with the exhaust pump. Connect the bell, cells and switch. Close the switch. 2. Start the pump and gradually evacuate the jar. 3. Stop the pump and let the air slowly return. 96. EXPERIMENTS ON SOUND Observations What changes in loudness are observed? Conclusion What would you be led to conclude about the ability of sound to be transmitted in the absence of a material medium? Questions 1. Why was sound not entirely eliminated? 2. What changes in the apparatus would improve this experiment? 3. What effect does changing the density of the medium have on the transmission of sound? 4. Verify your answer to question 3 experimentally, using different media, e.g., wood, water and air, between your ear and a sounding object, e.g., a waterproof watch. 5. Does light require a material medium for its transmission? EXPERIMENT 4 To illustrate the different kinds and fundamental characteristics of wave motion. (Ref. Sec. II; 5) Apparatus A length of rubber tubing, a long coil spring, two rigid supports. (a) Method 1. Tie one end of the rubber tubing to one of the supports. Tie a piece of string to the tube, leaving one end dangling. Vibrate the free end of the tube up and down with the hand. Note the effect of the vibration on the tube. 2. Attach the coil spring between the two supports. Tie a piece of string Squeeze several coils together and release them. to it as in part ( 1 ) Note the movements of the string. 97 Chap. 10 SOUND Observations 1. (a) What is observed when the end of the tube is vibrated? (b) What is the direction of the motion of the particles of the tubing relative to the length? 2. (a) What is observed when the coils of the spring are released? (b) What is the direction of motion of the coils of the spring relative to the length? Conclusions 1. What are the two parts of transverse waves? Define and give examples of transverse
wave-motions. 2. What are the two parts of a longitudinal wave? Define and give examples of longitudinal wave-motion. 3. Define; crest, trough, condensation, rarefaction, wave-train. 4. How is the energy from the source of disturbance transmitted through a medium? 5. What is the fundamental characteristic of wave-motion? Questions 1. What is the meaning of wave-length, the amplitude of the wave, the frequency of the wave, the period of the wave? 2. Establish the relationship between velocity, frequency and wave- length. EXPERIMENT 5 To show standing waves in a stretched cord. (Ref. Sec. 11:6) Apparatus Electric bell with gong removed, rigid stand and clamp, pulley and support, pan, with weights, length of light silk cord, batteries, connecting wire. Method Tie one end of the cord to the clapper of the bell and the other to the pan of weights. Assemble the apparatus as in diagram and close the circuit. Adjust the tension of the cord by changing the weights on the pan until the cord takes up a steady appearance. Observations 1. What effect has the clapper on the cord? 98 EXPERIMENTS ON SOUND 2. Wliat happens to this disturbance when it reaches the support at the distant end of the cordi’ 3. What is the appearance of tlie cord? Conclusions 1. What causes standing waves in a stretched cord? 2. Define; node, loop. Explain the cause of each. EXPERIMENT 6 To show what determines the pitch of sound. (Ref. Sec. 11:12) Apparatus Savart’s toothed wheel, rotator, cardboard card. Method 1. Assemble the apparatus as in Fig. 7:3 and rotate the disc while holding the card against it. Note the pitch of the sound produced. 2. Repeat part 1 while rotating the disc at a slower rate. 3. Repeat part 1 while rotating the disc at a faster rate. Observations What is observed in each of the above parts? Conclusion What determines the pitch of sound? Questions 1. How would you determine the frequency of the note produced in the above experiment? 2. What is the frequency of the note an octave higher than another? 3. What kind of sound would have been produced by a disc with irregularly spaced teeth? Explain. /Vote Experiment 6 may be done using a perfor
ated disc and a jet of compressed air. EXPERIMENT 7 To determine the law of lengths for vibrating strings. (Ref. Sec. 11:15) Apparatus Sonometer (Fig. 7:6), one steel string, movable bridge, tuning-forks with different frequencies such as 256, 320, 384, 512, 1024 v.p.s. Method 1. Using a string 100 cm. long, adjust its tension until the pitch of sound that it produces is the same as that of the fork whose frequency is 256 v.p.s. Record the frequency of this note and the length of string that produces it in the table below. 2. Without changing the tension, adjust the length of the string by 99 Chap. lO SOUND inserting the movable bridge beneath it. Determine the lengths of string that will produce notes of the same pitch as the other forks provided. Tabulate these frequencies and lengths. Observations 1. What length of string produces a sound of low frequency? 2. What change in frequency of sound occurs as the string is shortened? 3. Table of Results. Frequency OF Note Length of String Ratio of Frequencies Ratio of Lengths t Product of Frequency and Length of String 256 v.p.s. 100 320 v.p.s. 384 v.p.s. 512 v.p.s. 1024 v.p.s. Explanation 1. What is true of the ratio of the frequencies compared to the ratio of the lengths? 2. What is true of the product of the frequency of the note times the length of the string producing it? Conclusion State the law of lengths for vibrating strings.- Questions 1. In the above experiment, what length of string would have a frequency of 768 v.p.s., 128 v.p.s.? 2. In the experiment, what frequency would be produced by a string of length 150 cm., 20 cm.? 3. In part 1, what effect does changing the tension have on the fre- quency of the note produced? 4. List two factors that affect the frequency of a note produced by a vibrating string. EXPERIMENT 8 To illustrate the modes of vibration of vibrating strings, (Ref. Sec. II; 16) Apparatus Sonometer, one steel string, bow, several V-shaped paper riders. 100 EXPERIMENTS ON SOUND Method 1. Place three paper riders at equal intervals along the string. Bow the string at its centre and
note the effect on the riders and the pitch of the note produced. Record your results in the table. 2. Place three riders on the string as before. Touch the string lightly at its centre and bow the string in the middle of one of the halves. Make the same observ^ations as before and tabulate them. 3. Repeat part 2 using five riders, touching the string one-third of its length from one end and bowing in the middle of this third. 4. Repeat using seven riders, touching the string one-quarter of its length from one end and bowing in the middle of this quarter. 5. Repeat using nine riders, touching the string one-fifth the length of the string from one end and bowing in the middle of this fifth. Observations Position of Damping Effect on Riders Diagram to Si-iow Mode OF Vibration of String Frequency of Note Produced 1. None 2. 1/2 3. 1/3 4. 1/4 5. 1/5 1 1 Conclusions 1. What is the manner of vibration of a vibrating string when producing its fundamental? Its various overtones? 2. What are the frequencies of the various overtones compared to that of the fundamental? 3. Define: fundamental, overtone. Question How do you account for differences in quality of the same note from various sources? EXPERIMENT 9 To study the effect of the superposition of waves on the quality of sound produced, (Ref. Sec. II; 17) Apparatus Four tuning-forks (n = 256, 320, 384, 512 v.p.s.), rubber mallet, hard mallet, bow, tuning-fork on resonance box. Method 1. (a) Vibrate each tuning-fork separately by striking it with the rubber mallet and note the quality and pitch of the sound produced by each. 101'Chap. 10 SOUND (b) Vibrate the forks, n = 256 v.p.s. and 320 v.p.s., simultaneously and note the quality of the note. (c) Repeat part 1 one, two or three of the others. using the fork, n = 256 v.p.s., and with (b) 2. (a) Bow the -tuning-fork on the resonance box and observe the quality of sound produced. (b) Vibrate the same fork by striking it with the hard mallet and again note the quality of sound produced.
(c) Vibrate the same fork by bowing it and striking it with the hard mallet simultaneously. Note the quality of this sound. Observations What is observed in the above parts of the experiment? Conclusions 1. What determines the quality of sound? 2. Explain in terms of superposition of waves. EXPERIMENTIO To demonstrate resonance in a closed air column and to find the velocity of sound in air, (Ref. Sec. 11:20) > Apparatus Retort stand, clamp, cylinder, water, open tube about 15 inches long, several tuning-forks (256, 384, 512 v.p.s.). Method 1. (a) Fill a tall glass jar with water at room temperature to the three-quarter mark and place a smaller glass tube, open at both This tube should be clamped to a ends, in the water as shown. retort stand so that it may be raised, lowered or secured at will. Sound a tuning-fork {n = 256 v.p.s.) and hold it close to the open 102 EXPERIMENTS ON SOUND end of the tube. Raise or lower tlie tube until a position is found where the air column resounds most loudly. Measure the length of the air column. (b) Repeat (a) with the other tuning-forks. Observations 1. What was the room temperature? 2. What is observed when the tuning-fork is brought to the top of the tube before and after adjustment of the length? 3. Table of Results. Frequency of Fork Length of Closed Tube in Resonance 256 384 512 Explanation What is the cause of resonance? Calculations 1. What is the wave-length of the note produced by each tuning-fork? 2. Calculate the velocity of sound in air from the result obtained for each fork and average your answers. Conclusions 1. What is resonance? 2. What is the average velocity of sound in air? Questions 1. From the temperature recorded during the experiment, calculate the velocity of sound in air and compare it with the experimental value. 2. Determine the percentage error in your experimental result. 3. What is the relationship between the length of vibrating air column and the frequency of fork that gives resonance? EXPERIMENT 11 To study the production of sympathetic vibrations. 11:23) (Ref. Sec. Apparatus Two matched tuning-forks mounted on resonance boxes (Fig. 8:4), rubber mallet, wax
or plasticine. Method 1. Place the tuning-forks close together with the open ends of the Strike one fork and silence it after a short boxes facing each other. time. Note what happens. 2. Strike the other fork and repeat part 1. 103 Chap. 10 SOUND 3. Load the prongs of one of the forks with wax or plasticine. Sound the forks separately. What is observed? 1 and 2 using the forks as they are now. What 4. Repeat parts happens? Observation State your observations for each part above. Explanation Account for your observations. Conclusions 1. What are sympathetic vibrations? 2. Explain their cause. Questions 1. What would occur in this experiment if one fork were an octave higher than the other? Try it, and explain. 2. Suggest other examples of sympathetic vibrations. EXPERIMENT 12 To illustrate interference of sound waves by means of a study of silent points round a vibrating tuning-fork. (Ref. Sec. II: 24(a) Apparatus A tuning-fork, rubber mallet, closed air column as in experiment 10. Method 1. Vibrate the tuning-fork and hold it over the closed air column. Adjust the length of the column until resonance results. 2. Now slowly rotate the vibrating tuning-fork while holding it above the air column and observe. Observations Note the changes in the intensity of the sound heard and the position of the tuning-fork for each change. Fig. 10:7 Explanation With the aid of a diagram account for these changes. Conclusion What is meant by interference of sound waves? 104 EXPERIMENTS ON SOUND EXPERIMENT 13 To illustrate the interference of sound waves by the use of Herschel's divided tube, (Ref. Sec. II; 24(b) Apparatus Tuning-fork, rubber mallet, Herschel’s divided tube (Fig. 8:6), rubber hose and ear-trumpet. Method 1. Adjust Herschel’s tube so that the two paths CAD and C B D are equal. Hold a vibrating tuning-fork in front of the opening C and listen at the ear-trumpet joined to D. 2. Gradually draw out A and note the positions of minimum and maximum loudness of sound. Measure the difference in lengths of the two paths for each such position. Tabulate your results. Observations 1. Describe carefully what is heard. 2. Table of Results. Intensity
was struck a glancing blow with a sharp piece of flint (a hard, compact mass of silica, the mineral of which sand is composed). Both of these are a far cry from the use of such modern devices igniters etc., although ihe principle of the flint gas and still employed in as matches, electrical igniter is cigarette lighters. The many developments in the production of heat that have occurred since early times give ample evidence of man’s creativeness. Equally interesting are the forward strides made in the understanding of the nature of heat and the laws that govern its use. Not only has man learned how to produce heat but he can now control it, retain it, measure it, transfer it from place to place and convert it into motive power. This study of heat is sufficiently large and important to warrant a special branch of physics, namely, “thermodynamics”. Ill : 2 THE NATURE OF HEAT (a) Caloric Theory Until well into the nineteenth cen- in most the spite people believed tury, Caloric Theory of Heat in of questionable proofs to support it. This theory insisted that all empty spaces in matter contained a fluid called caloric and that the warming or cooling of a body was due to the gain or loss in the amount of this fluid. The early Greeks speculated that heat was the rapid vibratory motion of the molecules of a body. Francis Bacon produced some promising experimental evidence to (1561-1626) this effect. In an 1798 American, Benjamin Thompson, who later became Count Rumford, made further investigations. While directing the boring of cannon, he became interested in the amount of 109 Chap. 11 HEAT heat produced in the process and decided to investigate the problem of the nature of heat. The adherents of the caloric theory argued that caloric came out when iron shavings were formed and that the shavings had more of it than the iron. To test this theory, he applied a blunt drill (to produce few shavings) to the cannon with the whole assembly immersed in a box filled with water. In a short time the assembly became warm and finally the water boiled. Because heat was long the mechanism continued to turn, Rumford concluded that anything which could be as heat had produced without limit, been, could not be a material substance (caloric). He reasoned that heat must be caused by a vibratory motion in the produced as as material. In 1799 Sir Humphrey Davy of England dealt the caloric theory the
coup de grace by rubbing together two pieces of ice in a vacuum at a temperature The below the melting-point of caloric theory held that as ice contained no caloric it could not melt under these conditions. But melt it did and in doing so afforded yet more proof that heat must be a product of motion. ice. (h) The Kinetic Theory of Matter According to theory, matter is this composed of numerous, tiny, moving called molecules, each being particles separated from its neighbour by empty space. A molecule is defined as the smallest particle of a substance which can exist alone and possess the properties of that substance. Scientists are forced to accept such a theory because they know that gases, and to a lesser extent liquids and solids, diffuse, and that gases do not settle but maintain a uniform pressure on the walls of the container. All the evidence indicates that molecules of gases are separated by comparatively vast distances, e.g., water vapour molecules are no more than ten times as far apart as water molecules, and possess great freedom of movement. Molecules of liquids have freedom of movement but must be fairly close together, since liquids resist compression. In solids the molecules exhibit great cohesion as illustrated by their rigidity. Their closeness is shown by their resistance,to compression. Their movement is said to consist of vibration about certain positions in a prearranged pattern. (c) Heat—A Form of Energy Energy is the ability to do work. All moving bodies can do work and therefore have energy. Heat, which is caused by the motion of the molecules of a body, is capable of doing work and therefore must be a form of energy. THE NATURE AND SOURCES OF HEAT Sec. 111:3 that This may be illustrated with the aid of the apparatus shown in Fig. 11:1. When the tube is heated an effect is imitates somewhat the observed motion of the molecules. The mercury vaporizes and the molecules of mercury vapour drive the bits of glass upward. The pieces move about erratically, colliding with mercury molecules and each Heat is causing the motion of other. the particles (molecules and glass) and hence heat must be a form of energy. Under other circumstances heat energy may be transformed into other forms of energy such as electricity, light, etc. if from the Law of Conservation of Energy. This fundamental law of nature states that energy can neither be created nor destroyed although it may be transformed into any of its many forms. In a moving automobile is practice, brought to a stop by
its brakes, the disappears enei‘gy changes to heat energy in the brakes. From this and numerous other examples, it is evident that heat is produced at the expense of some other form of energy. A brief discussion of several sources of heat (Fig. 11:2) will follow. motion which of (a) Mechanical Action Ill : 3 SOURCES OF HEAT The origin of heat may be inferred In every mechanical operation, the output of work is always somewhat less (a) MECHANICAL (a) MECHANICAL (a) MECHANICAL Compression (c) ELECTRICAL Combustion Fig. 11:2 Sources of Heat. Ill Chap. 11 HEAT than the input of energy, the loss being equal to the amount of energy converted into heat. This is stated thus: input = output -\|- heat. All such operations involve friction, because no surface is perfectly smooth. When one body slides or rolls over another, as when the hands are rubbed together, some of the energy devoted to the purpose is converted to heat. Frequently, percussion, which is the sudden stopping of a moving object when it collides with one at rest, e.g., hitting a nail, is employed in mechanienergy of cal motion is converted into molecular motion within both bodies which is mani- Here the operations. fested as heat. Some operations involve compression of gases. We know from operating a bicycle pump that some of the energy applied changes into heat. In the Diesel engine (Sec. 111:31), the heat produced by compression of the air in the cylinder is sufficient to ignite the fuel. (h) Chemical Change When a fuel is burned in air, new are formed and energy is materials released. Such a happening is called a chemical change. Every substance has its share of stored chemical energy, a form of potential energy, and when it burns the products of combustion generally possess less of it than do the original materials. The difference in the amount two represents changed into heat. For example: energies the (c) The Electric Current it This Whenever a conductor carries elecbecomes warmer. tricity, is because electrical energy encounters resistance to its flow in much the same way as water encounters resistance (friction) while flowing through a pipe. Just as the moving water loses energy as it overcomes resistance, so too does an electric current. The electrical energy lost becomes transformed into heat. Heatingelements clearly demonstrate this. (d) The Atom All matter in the
universe is made up from about one hundred different kinds of elements. Elements are simple substances that have not been decomposed by ordinary chemical means. They are composed of atoms which are the building-blocks for the molecules of all sub- like those Some atoms, this energy. of stances. uranium or radium, are very large and complex and change into new atoms As they do so a small spontaneously. amount of mass changes into energy some of which becomes heat. There are more details of this process in chap. 32. Huge structures called atomic piles conContrary to popular trol belief, the energy from this source is not amazingly limitless large. For example, it has been estimated that one pound of uranium can produce three million times as much energy as one pound of coal or one pint of oil. Imagine how little uranium would be required to heat your home for one year! nevertheless, but, fuel + oxygen carbon dioxide + water + heat. The total energy of the fuel and of the oxygen equals the total energy of the carbon dioxide and of the water plus the energy which was converted into heat. 112 (e) The Sun Few of us realize the importance of the sun as a source of energy. We accept its daily warmth, and take for granted its energy stored in plant and animal products, in the water vapour of the air, in water and air currents, and in the THE NATURE AND SOURCES OF HEAT Sec. Ill: 3 Fig. 11:3 Trapping Solar Energy. fossil fuels—oil, coal and gas. If the sun were to be suddenly extinguished and all the sources of energy at our disposal were tapped at one time, our accustomed temperature would be maintained for After that we would only three days. quickly freeze to death! In spite of the fact that the earth is only a tiny dot in space, it receives a million-trillion kilowatt hours (Sec. V:75) of energy per year, of which all but.05 per cent slips from our grasp. Green plants trap the major part of this percentage, as follows: carbon dioxide + water + light energy (in the presence of chlorophyll) carbohydrates + oxygen This process is known as photosynthesis. The sun’s internal temperature, estimated at about 20 million degrees centi- grade, is maintained by a complicated process which is essentially the union of 4 atoms of hydrogen to form 1 atom of helium gas. Dr. Hans Bethe at The Bell Telephone Company of Canada. Fig. 11:4 The Solar Battery
. 113 Chap. 11 HEAT Cornell University in 1938 showed that there is a decrease in the mass during the process and that this is converted to heat. For some time man has dreaded a world scarcity of fuel, knowing that at our present rate of consumption we shall be at that critical point in two or three centuries. Accordingly, research workers are constantly seeking ways and means of using solar energy. Some pin their hopes in part on utihzing an improved photosynthetic process, while others are investigating the use of light-sensitive 11:3, 11:4). As the chemicals (Figs. sun will yield its fabulous supply of energy at the present rate for an estimated 10 billion years, our future is assured, provided inexpensive ways and means of sunlight can be found. collecting that III : 4 QUESTIONS A 1. (a) Present an argument to show that heat is a form of energy. (b) Describe the changes in size and state that occur on intensely heating a piece of iron. Explain each by means of the kinetic theory of matter. 2. Explain each of the following: (a) A bullet is found to be warmer after hitting a target. when concentrated sulphuric acid is added to water. (d) A fuse burns out in an overloaded electrical circuit. (e) The origin of heat from the splitting of the atom. (f) The origin of energy from the sun. 3. State all the energy transformations that are involved in the sequence: sunlight, water-power, electricity, heat from a toaster. (b) Bearings frequently "burn out" when they run short of oil. (c) Considerable heat is produced 4. If the heat from 6 tons of coal will heat a home for one year, what mass of uranium (U235) will do the same thing? 114 CHAPTER 12 EXPANSION CAUSED BY HEAT (Fig. 12:2) consists of equal lengths of iron and brass welded together. On being heated, the bar bends with the III : 5 EXPANSION OF SOLIDS Almost all bodies expand on being heated and contract on being cooled. The ball and ring experiment (Chap. 15, Exp. 1), demonstrates the expansion and contraction of metals (Fig. 12:1). That different metals expand and contract by different amounts when heated or cooled through a given change of Fig. 12:2 Unequal Expansion of Solids. Since the brass on the outside. distance round the outside of a curved path
.000019 0.000026 0.000019 0.0000009 0.000011 0.0000088 0.0000085 0.0000004 0.0000036 *Pyrex consists of 80 per cent silica and 20 per cent various oxides of metals, chiefly of boron. 111:6 APPLICATIONS OF EXPANSION OF METALS Some applications of expansion have been mentioned already and it is clear that the expansion of metals, though small, must always be taken into consideration. The errors in using metal surveying tapes have been largely overcome by the use of invar steel, a nickel-steel alloy containing 36 per cent of nickel and having a coefficient of linear expansion which is almost negligible. The same material is used for the pendulums of clocks to ensure almost constant length and accurate time-keeping. Watches are controlled by a metal balance-wheel (Fig. 12:3b) and hairoscillation of the spring, wheel being determined by its diameter. A rise in temperature would cause the diameter of the wheel to increase and. the time of consequently, the watch would lose time. To compensate for this defect the rim of the wheel is made in segments, each being a bimetallic strip of brass and steel with the more expansible metal on the outside. When the temperature rises, the segments curl inward, reducing the “efthe wheel and fective of compensating for the troublesome increase in diameter that would otherwise occur. diameter” strip, with The principle of the bimetallic strip finds other applications. One is the dial thermometer (Fig. 12:4a). The essential part of this instrument is a coiled bithe more again metallic expansible metal on the outside. One end of the coil is firmly attached to the case of the instrument and the other is connected to the pointer. As the coil winds or unwinds with a rise or fall in temperature, the movement of the free end is transmitted to the pointer moving over a scale graduated in degrees. Although not as accurate as other thermometers to be described in Sec. Ill: 8, is a robust instrument and has the it advantage of containing no liquid to vaporize or solidify. Such a device is also an essential part of the thermograph or Fig. 12:4 (a) The Dial Thermometer. 117 Chap, 12 HEAT fb) The Thermo- graph. Compound Bar continuous recording thermometer (Fig. 12:4b). Thermostats for automatically regulating
the temperature will be constructed. The temperature of a body may be defined as that condition which determines the direction of heat flow between it and its surroundings. Thus, a body at a high temperature will give heat to cooler objects while a body at a low temperature will take in heat from warmer objects. This will proceed until all objects are at the same final temperature. (b) Thermometers Originally, man relied solely on his 119 Chap. 12 HEAT sense of touch to measure temperature. Obviously, judgments obtained in this way are not very precise. For example, a door-knob feels colder to the touch than the wooden door. Again, if one hand is placed in a beaker of hot water, and the other in a beaker of cold water, and then both hands are placed simultaneously in lukewarm water, the first hand will get the impression of coolness and the second that of warmth. Clearly, i'* B W Fig. 12:8 Filling a Mercury Ther- mometer. scale therefore, some means of measuring temperature that is more sensitive and more reliable than that provided by human sensations is needed for scientific purposes. We must have a precise, conof temperature and an sistent instrument for measuring it accurately. The evolution the modern thermometer is an interesting story. Students are advised to consult a good encyclopedia for the contributions of such men as Galileo, Viviani, Rey, Boulliau and others who have shared in its perfection. of 120 to register rapidly. The modern thermometer is constructed from a length of capillary tubing of uniform bore, sealed at one end by heating it in a flame. By gently blowing down the tube when it is hot, a small bulb is produced at B (Fig. 12:8). This should be very thin if the instrument ‘is After the tube has cooled, a small funnel is attached to the open end A, and clean dry mercury is poured into it. Before the mercury will fill the bore it is necessary to heat and cool the bulb alternately to force the air past the metal. When the tube is full, it is heated to expel any remaining traces of air. The bulb is now placed in a bath of liquid which has a tempera15° higher than the ture 10° of to ther- temperature which the highest mometer will be required to register. Using the fine blow-pipe flame, the tube is sealed at a point just below the free surface of the mercury. On removing the thermometer from the the mercury contracts in
the stem, leaving a vacuum in the space above it. bath, To graduate the thermometer, we choose two fixed temperatures which can be easily obtained, and mark the level of the mercury on the stem when each of these temperatures has been maintained for some little time. The temperatures chosen are the freezing- and boiling-points of pure water at standard atmospheric pressure (760 m.m. of mercury). The former is called the lower fixed point and is marked on the stem by making a groove in the glass with a file at the level of the mercury when it has been standing for some time in melting ice (Fig. 12:9a). To obtain the upper fixed point, the thermometer is placed in the apparatus shown in Fig. 12:9b where the bulb and stem are surrounded by steam. When the mercury level is stationary the upper fixed point is scratched on the stem. If the pressure is not standard, it is necessary EXPANSION CAUSED BY HEAT Sec. Ill: 8 i to apply a correction before making this mark. 100°C. Upper Fixed 212°F. Having determined the positions of the fixed points, we divide the distance n V Point f 100 divs. C. = 180 divs. F. ^.'. 1 div. C. = — div. F. 9 0°C. Lower Fixed k 32°F. Point CENTIGRADE SCALE FAHRENHEIT SCALE Fig. 12:10 Comparison of Temperature Scales. Daniel Gabriel Fahrenheit (16861736), a German instrument maker at Amsterdam, selected points 212°F. and 32°F. and constructed the scale that bears his name. In choosing fixed the >-55C.° 100°C. 45°C. 30°C. 15°C. °C or Actual Temperatures Changes in Temperatures or Fig. 12:11 The Comparison of °C and C°, 121 j grees. Then we test the thermometer I at various temperatures against a stan- dard instrument for accuracy. II - (c) Temperature Scales Two thermometer scales, the Fahren! heit and Centigrade or Celsius are in common use in English-speaking countries. The former is used in everyday practice while is used in science. In countries that are not English-speaking the centigrade thermometer is used for all purposes. latter the i, 'I I Chap. 12 HEAT those fixed points, he was influenced by the incorrect thought that 0
°F. was the lowest temperature that could be reached. The centigrade scale introduced by the Swedish scientist Celsius, in 1742, had the fixed points of 100°C. and 0°C. boilingrepresenting, and freezing-points of pure water. respectively, -the The comparison of these two scales may be seen by reference to Fig. 12:10 and with its help we are able to convert a temperature on one scale to a corresponding temperature on the other. However, before we attempt any con- versions it should be stressed that °C. and °F. refer to actual temperatures whereas C.° and F.° refer -to a change of temperature anywhere on the scale. For example, difference between 15°G. and 15C.° is shown in Fig. 12:11. the (d) Conversion of Temperatures both scales Since temperature are legal, it is important that we be able to convert a centigrade reading into the corresponding Fahrenheit reading, and vice versa. The following examples will show how this is done. Examples 1. Convert 20°C. to a Fahrenheit reading. 20°C. is 20C.° above the freezing-point (0°C.) 100C.° = ISOF.r 100 20C.° = 20 X - = 36F.° 5 5 20°C. is 36F.° above the freezing-point (32°F.) 20°C. = (32 + 36) = 68°F. 2. Convert 14°F. to a centigrade reading. 14°F. is 18F.° below the freezing-point (32°F.) 180F.° = 100C.° lF.o=l^ = ^C." 180 9 18F.° = 18 X - = 10C.° 9 14°F. is 10C.° below the freezing-point (0°C.) 14°F. = (0 — 10) = — 10°C. The above conversions may be accomplished more conveniently by applying the following formula: not to attempt to use the formula until they have mastered the previous solu- tions. °C. =^(°F. -32) However, it is only by a study of the foregoing examples that the reasons for the various operations in the formula will be understood. Students are advised Ill ; 9 EXPANSION OF GASES You will remember from your earlier studies of science that gases expand on heating and contract on cooling
(Fig. 12:12). In addition, you will recall that gases expand much more than liquids 122 EXPANSION CAUSED BY HEAT Sec. Ill: 9 and solids for a given change of temperature, i.e., they have a greater coIt may seem expansion. efficient of Fig. 12:12 Expansion ond Contraction of Gases. strange, but is nevertheless true, that all the same gases have This may be coefficient of expansion. exactly almost expressed thus: “At constant pressure, the volume of a given mass of gas Increases by 1/273 of its volume at 0°C. for each centigrade degree rise in temperature”. It should be noted that, because gases are compressible, constant pressure must be relationship prescribed this for to hold. A special use of the coefficient of expansion of gases is in determining “abIf we were provided with solute zero”. a tube containing 273 c.c. of gas at 0°C. it would contain 263 c.c. at — 10°C., 200 c.c. at — 73°C., and theoretically, 0 c.c. at — 273°C. We know, of course, that we cannot destroy matter in this way and the gas would have changed in that state before reaching this temperature. This temperature, — 273°C., is called absolute zero, a temperature at which bodies all molecular motion having ceased. More accurately, absolute zero is — 273.16°C. The lowest temperature so far recorded is.005° above absolute zero. possess no heat whatever, Absolute zero is the lowest point on another temperature scale, the Absolute or Kelvin Temperature Scale, first proposed by Lord Kelvin, a great English scientist (1824-1907). This finds application in the calculation of the volumes of gases and will be used extensively for that purpose in your chemistry course. Fig. 12:13 shows the relationship between centigrade and Kelvin tempera- 273'^C. 546°K. I00°C. -- 373°K. 0°C. -- 273°K. -273‘’C, J- 0°K. Fig. 12:13 Comparison of Centigrade and Kelvin Scales. tures. You will see that to obtain a Kelvin temperture 273 is added to the centigrade reading. 123 Chap. 12 HEAT A practical application of the effect of heat on the volume of a gas is shown in rise the pressure
12:12, the instrument is sealed so that the gas is maintained at constant volume and a rise in temperature causes a proportionate (Fig. This pressure change is read 12:14). directly in degrees. For low temperature work hydrogen or helium is used. Above 500°C. they would diffuse through the bulb and for this reason nitrogen is This device is used to used instead. calibrate thermometers. Ill : 10 THE EFFECT OF EXPANSION ON DENSITY Since changes in temperature cause changes in volume without affecting the mass, densities of substances vary with the temperature. When heat is applied, substances usually expand and a decrease Substances are said in density occurs. to be “lighter” then. The opposite effect occurs when they are cooled. A few exceptions to this rule are known, the most outstanding being water. As was shown in Sec. 1:6, water contracts when its temperature rises from 0°C. to 4°C. and thus its density increases. This is known as the anomalous behaviour of water. Above and below these temperatures water behaves normally. in the gas thermometer. Instead of allowing the gas to escape as in Fig. Ill : 11 QUESTIONS 1. 2. A (a) A threaded metal cover on a glass sealer fits too tightly. How may it be released? Explain your method, (b) What error would be introduced a into surveyor’s tape made of copper? What material is used to avoid such errors? Why? measurement by using a explain and (a) Describe happens when a bimetallic strip heated and then cooled. (b) What is purpose of the what is the 124 balance-wheel of a watch? How does it accomplish its purpose? (a) How is a centigrade thermometer scale calibrated? (b) Under what conditions is mercury preferable to alcohol as the liquid in a thermometer? Give reasons for your answers. (a) When would gases be used in thermometers? Where and when are such thermometers used? (b) What is absolute zero? (a) Define linear and cubical efficients of expansion. co- 3. 4. 5. EXPANSION CAUSED BY HEAT Sec. Ill: 11 (b) Why does increasing the temperature usually cause a decrease. in the density of a substance? B 1. Find the readings on the Fahrenheit thermometer corresponding tol5°C., 200° C, -60°C, -273°C
2. Find the readings on the centigrade Fahrenheit thermometer scale when the reads: 100°, 350°, -220°, -50°. Fahrenheit and centigrade readings the same? (b) At the Fahrenheit reading double the centigrade reading? temperature what is 4 (a) (i) Express 57°C, — 23°C as Kelvin temperatures. (ii) Convert 298°K., 237°K. to centigrade temperatures. (b) (i) Express 98°F., 0°F. as Kelvin temperatures. (ii) Convert 373°K., 0°K. to 3. (a) At what temperature are the Fahrenheit temperatures. 125 CHAPTER 13 TRANSFER OF HEAT is transmitted from molecule to molecule along the length of the bar until the far end becomes hot. Metals are generally good conductors of heat, some better than others. The differences in the conductivities of four different metals may be shown by performing experiment 3, chapter 15, using a conductometer similar to that shown in Fig. 13:1. The relative conductivi- ties of some common metals are shown (The figures used in the in the table. table indicate the number of heat units, calories, conducted in one second by a cube 1 cm. to the edge for each centigrade degree.) III; 12 HOW HEAT IS DISTRIBUTED In a previous chapter we studied the sources of heat energy. Here we shall learn how heat is conveyed from the source so that it may be made to go where it is required, or prevented from is not needed. When a going where it saucepan touches a hot stove it becomes warm: heat has travelled by conduction. The current of warm air above a hot radiator is carried upwards by convection. A fire-place sends out heat by radiation. Thus, the three methods of heat transfer are; conduction, convection and radiation. Ill : 13 CONDUCTION (a) Solids If one end of an iron bar is placed in a fire, the other end will soon become warm. The heat energy has been transferred along the bar by the process of conduction. The rate of vibration of the molecules at the hot end, and therefore their energy, has been greatly increased, and this results in the molecules in sucbar acquiring cessive increased energy by the chain of colliIn this manner heat sions that results. sections the of 126 TRANSFER OF HEAT Conductivities of Some Common Substances Alcohol Petroleum
the poor conductivity of liquids does not include mercury, which, being a metal, is a good conductor. (c) Gases If the hand is held close to a Bunsenburner flame, the resulting burn is not as intense as when gripping a metal bar at the same distance from the flame. This demonstrates that air (or any gas) is a poor conductor of heat. When we recall that gases are composed of molecules that are very far apart and that heat conductivity depends on the actual contact between molecules, we understand why gases are poor conductors of heat. The above fact concerning gases has many practical applications. In part (a) of this section, reference was made to certain solid insulating materials with loose texture. Many of these, such as fur, wool, sawdust, rock wool, asbestos, snow, etc., depend on the poor conductivity of pockets of air trapped in them for a large insulating properties. Storm-windows, thermopane and the hollow construction of the outer walls of buildings (Fig. 13:2) likewise have insulating value because of the poor heat conductivity of the enclosed their part of air. Ill : 14 CONVECTION (a) Liquids (Chap. If a small crystal of potassium permanganate is dropped into a beaker of cold water heated gently by a Bunsen red burner 15, streaks will be observed as the crystal dissolves (Fig. 13:4). The streaks will rise, move just under the surface of the water for some distance, and fall. Some of the colour may be seen to return to 4A), Exp. TRANSFER OF HEAT Sec. 111:14 If we realize that its point of origin. different parts of the liquid in the beaker have different temperatures, then the streaming of the colour signifies that there are rising and falling currents in the water caused by these differences in temperature. These currents are known as convection currents and are the means by which the heat is circulated through water and liquids. The movement is established because of the expansion and consequent decrease in density of the water immediately above the source of heat. The mass of hot water is being pushed up continually and replaced by the surrounding denser water. Convection, then, is the transfer of heat in a substance by the actual, sometimes observable, motion of its parts. It should Fig. 13:4 Convection Currents in Liquids. Fig. 13:5 Applications of Convection Currents in Liquids. (a)
, the land will cool faster by radiation (Sec. 111:15) and the reverse in a land- situation will results. result breeze (i.e., off-shore). Hot-air heating systems (Fig. 13:8) depend upon convection currents for However, both the transfer of heat. bution of heat on cold windy days, when it is hard to heat the windward This situation is side of the building. largely corrected by the use of “forcedair” heating where a motor-driven fan This system accomplishes the transfer. has the further advantage that the air is “conditioned”, that is, dust is filtered out and the humidity is more efficiently Fig. 13:8 Hot-air Heating (a) Pipeless (b) Conduit Type (c) Forced-air. 131 Chap. 13 III : 15 RADIATION (a) Introduction HEAT tions, When you stand before a camp-fire, you are aware of its intense heat. Since the effect may be prevented by holding up a blanket between yourself and the fire, you will conclude that the energy travels in straight lines. Since the same thing happens on all sides of the fire, this energy must radiate in all direci.e., travel along the radii of a sphere with the fire at the centre. This kind of energy is a form of radiant energy and the method of transfer is It is only when this called radiation. energy strikes an object and is absorbed that it changes to heat energy. Transfer of energy by radiation is different from conduction and convection since the latter require a material medium, whereas radiation may proceed through a vacuum. For example, radiant energy from the sun traverses 93 X 10® miles of space, most of which is empty. Or again, energy may radiate from the filament to the glass envelope of an evacuated radio tube. Radiant energy is a wave-motion and has many properties in common with is the radiation light. The major heat effect comes from the infra-red radiations just beyond the red of the visible spectrum (Sec. IV: 38). Subsequent references to radiant energy in this section refer to these infra-red radiations. All bodies whose temperatures are above absolute zero (Sec. III:9) emit this kind of energy at the expense of the energy of motion of their atoms or molecules. The rate of emission and the wave-length of proportional to the temperature: the higher the temperature, the faster the rate and
the shorter the wave-length. The waves are believed to be of the transverse variety which, according to one theory, are set up by a minute pulse of energy, called a quantum, from the source. These waves are a part of the great electromagnetic family of waves (Fig. 19:4) that includes visible light. X-rays, ultraviolet rays, radio waves, cosmic rays, all of which have a velocity of etc., 186,000 miles per sec. For their transmission, early physicists invented an imaginary, weightless, all-pervading medium called ether, but the Theory of Relativity proposed by Einstein denies its existence. The nature of the medium still remains a mystery. 132 Light Surfaces. TRANSFER OF HEAT Sec. 111:15 (h) The Emission of Radiant Energy (c) The A bsorption of Radiant In the introduction to this section, it was stated that radiant energy is released at the expense of motion of the molecules. It may well be asked whether or not all objects under the same conditions emit this form of energy. To find the answer, experiment 5, chapter 15, should be performed. For the purposes of discussion, let us take two cans (Fig. 13:9), one dark and dull on the outside, the other light and shiny, but identical in other respects. Energy As this objects absorb previously, was suggested heat results when radiant energy is absorbed. A critical thinker will want to know if energy different equally well. To answer this in part, experiment 6, chapter 15, should be performed. Another demonstration (Fig. 13:10) involves two thermometers, one darkened and dulled by the soot from a candle flame, the other left light and shiny, placed at equal distances on either side of a source of heat such as a Bunsen burner. The temperature of the one with the dark, dull surface rises more quickly than that with the light, shiny surface. We know that dark, dull surfaces absorb light without reflecting much of it and a light, shiny one reflects most of the light without absorbing much of it. In Comparing the Ability of Fig. 13:10 Dull Dark and Shiny Light Surfaces to Absorb Radiant Energy. Place a quantity of hot water and a thermometer in each and support them Although on identical insulating-bases. both are at the same temperature initially, the water in the dark, dull can cools more quickly than that in the light, shiny one. No matter how we perform such
an experiment we always find that dark, dull surfaces are good emitters of radiant energy, while light, shiny ones are poor in this respect. It is admitted that other factors, such as starting temperature and area of surface also affect the rate but for the purpose of our discussion, these were kept constant. Can Pratt and Whitney Aircraft. Radial Engine of Airplane. Note cooling fins on cylinders. the same manner dark, dull surfaces are good absorbers and poor reflectors of radiant energy, while light, shiny sur- 133 Chap. 13 HEAT faces are poor absorbers and good reflectors. Knowing this we wear lightcoloured clothes in summer and dark ones in winter. (d) The Transmission of Radiant Energy are Certain materials “transparent” or “opaque” toward radiant energy just as some are toward light. As an example, ice does not transmit much radiant energy, while rock salt transmits almost all that falls upon it. Glass, on the other hand, transmits well the shorter wavelengths that originate from a high-temperature source like the sun but does not transmit the longer ones that originate from a low-temperature source such as the earth or a living object. This property of glass makes it greenhouses (part (f) below). useful in (e) Some Detectors of Radiant Energy The simplest device is the darkened air-thermometer, or thermoscope, where radiant energy is converted into molecular motion which manifests itself as a rise of temperature (Fig. 13:11a). The radiometer (Fig. 13:11b) consists of an almost completely evacuated glass bulb in which four light aluminum vanes are mounted so as to turn easily. One side of each vane is blackened while left shiny. When radiant the other is energy falls upon the vanes, the black surfaces become warmer than the others. Accordingly the few air molecules adjacent to the black sides will become heated and will move away from the vanes. The reaction of the vanes causes them to turn about their pivot. The more radiant energy that enters, the faster will the vanes turn. This instrument is very sensitive to small amounts of radiant energy. 134 Fig. 13:11 Some Detectors of Ra- diant Energy, (a) Thermoscope. (b) Radiometer. (f) Applications of Radiant Energy The vacuum or thermos bottle (Fig. 13:12) is a double- walled glass bottle, with a high vacuum between the walls
, contained in a suitable protective carrying case. The inner glass walls facing each other are silvered. Liquids, whether hot or cold, will remain at very nearly the same temperature for several hours. The reason is that the bottle is so constructed that it is very difficult for heat to be transferred by any of the three methods described above. We shall consider the storing of a hot liquid here. Similar explanations obtain for a cold liquid. 1. The vacuum prevents the loss of heat by conduction owing to the lack of molecules present. The transfer of heat through the glass and the stopper is slow owing to the poor conducting property of each. 2. Convection from inside the bottle TRANSFER OF HEAT Sec. 111:15 reflected back inside. Thus, these devices act as heat traps for the energy from the sun. A further application, the screening action of the clouds, depends on the inability of water to transmit radiant upwards is prevented by the stopper. Loss by convection in the air space between the glass and the case is prevented by being closed at the top. 3. Heat loss by radiation is prevented by the silvered surfaces of the walls. These reflect back into the bottle any radiant energy that tends to escape. Greenhouses and cold frames (Fig. are heated by radiation. The 13:13) short wave-length radiant-heat energy from the sun is readily transmitted by the glass. This is absorbed by the plants, etc. within; as their temperatures soil, rise, they lose heat by radiation. Since this longer wave-length radiant energy is not transmitted by the glass it is largely Shiny Metal Cap Cork Stopper Double-Walled Glass Bottle Silvered Inside Vacuum Silvered Outside Metal Case Spring Felt Fig. 13:12 The Thermos Bottle, Fig. 13:13 A Greenhouse Acts as a "Fleat Trap". well. The moisture energy present in the atmosphere absorbs much of the sun’s heat by day, thereby preventing the scorching of plant and animal life. At night the clouds provide a blanket which prevents the escape of radiation from the earth’s surface, the temperature of which is largely maintained. On the other hand, in hot, dry, arid regions, the absence of water vapour results in extreme temperature changes, being very hot by day and very cold by night. We have included these few applications for their general appeal since they come within the realm of everyone’s experience. However, many other applications are to be found both in nature and
elsewhere. It is to be hoped that with this introduction to the subject, the student will be able to recognize others as he encounters them. 135 Chap. 13 HEAT Installation for radia heating ant in building. Anaconda American Brass Ltd. III : 16 QUESTIONS 1. Name three methods of heat transfer and explain how they are involved in heating water in a kettle over an electric (b) Should the bottom of a kettle be polished for economical heating? Explain. 5. Make a chart comparing conduction, convection and radiation, under the following headings (a) the media in which the transference takes place, (b) direction of the transference, (c) a brief comparison of the theories which explain how the transference occurs. 7. 6. Explain the action of a radiometer. (a) Make a labelled diagram of a thermos bottle. (b) Write a note to show how (i) conduction, (ii) convection, (iii) radiation are reduced to a minimum when a hot liquid is placed in the bottle. heating-coil. it, in fact, 2. (a) On a cold day, why does the metal door handle feel colder than the wooden door? Is colder? (b) Name three good conductors and three good Insulators of heat, and state the use for each. (a) What are convection Explain how they are produced. (b) Explain the production of an on- currents? 3. shore breeze. 4. (a) Why does more rapidly when dirty, than when clean? snow melt 136 CHAPTER 14 MEASUREMENT OF HEAT III; 17 WHY WE MEASURE HEAT We know that heat is a form of energy (Sec. Ill :2c) and that other forms of energy can be changed into heat, but why do we bother to measure it? Were we required to determine the efficiency of an electric heater, the energy yield when a gallon of gasoline, a pound of tablespoonful coal sugar or of is a Fig. 14:1 Distinction between Quan- tity of Heat and Temperature. burned, we should be able to measure the quantities of heat produced. Various fuels and foods are used widely because of their large energy content. Hi: 18 THE COMPARISON OF QUANTITY OF HEAT AND TEMPERATURE When two equal masses of water are heated by the same source for the same length of time, each will show the same If the experiment rise in
temperature. is repeated with one mass larger than the other (Fig. 14:1), the smaller mass will show a greater rise in temperature. If two unequal masses of water are heated to the same temperature by the same source, the larger mass will require to be heated for a longer time. is evident that temperature and quantity of heat are entirely different and should never be confused. It Ill : 19 FACTORS THAT INFLUENCE THE QUANTITY OF HEAT We are all familiar with the fact that a basin of hot water may be cooled by the addition of cold water and that the final temperature of the mixture will be lower than that of the hot water and higher than that of the cold. We realize that the hot water becomes cool as ft gives heat to the cold water while the cold water becomes warm because it gains heat from the hot. This is the principle of heat exchange and it applies whenever substances at different temperatures are mixed (Sec. 111:22). 137 Chap. 14 HEAT : at each different equal masses of water, Let us mix two equal masses of water, with temperatures, the same at Since the warmer water temperature. gives rise to the higher final temperature (see example), the mass at the higher temperature obviously contains the greater quantity of the heat. quantity of heat contained in a body varies as its temperature. For example: When 100 gm. of water at 80 °C. are added to 100 gm. of water at 20°C., the final temperature is 50° C. When 100 gm. of water at 40°C. are added to 100 gm. of water at 20°C., the final temperature is 30°C. Therefore, Let us mix two different masses of water, at the same temperature, each with equal masses of water, at the same temperature. As the larger mass gives rise to the higher final temperature (see example), it follows that the larger mass larger quantity of heat. contains the Thus, the quantity of heat contained in a body varies as its mass. For example: When 100 gm. of water at 80° C. are added to 100 gm. of water at 20°C., the final temperature is 50°C. When 200 gm. of water at 80°C. are added to 100 gm. of water at 20°C., the final temperature is 60° C. So far, we have dealt with quantities of water in the above examples, but what would be the effect of using one different substance along
with water? us mix two equal For example, let masses, one of water and one of iron filings, at the same temperature, with two equal masses of water, also at the same temperature. The water will give rise to the higher final temperature (see example), because it contains more heat than the iron. Hence, the quantity of heat contained in a body depends upon the nature of the material of which it is composed. For example: When 100 gm. of water at 80°C. are added to 100 gm. of water at 20°C., the final temperature is 50°C. When 100 gm. of iron filings at 80° C. are added to 100 gm. of water at 20°C., the final temperature is 26°C. Ill : 20 THE UNITS FOR MEASURING THE QUANTITY OF HEAT Because water is a common substance and its capacity for heat is so great, it is used as a reference material in defining the units for measuring the quanIn the metric system, the tity of heat. unit of quantity of heat is the calorie. A calorie is the quantity of heat gained or lost when the temperature of one gram of water rises or falls one centigrade degree. How many calories of heat are gained by 100 gms. of water when its Example temperature rises from 20°G. to 80°C.? Change in temperature = 80 — 20 = 60C.° Quantity of heat required to raise the temperature of 1 gm. of water 1C.° = 1 cal. 100 gm. of water 1C.° = 100 X 1 = 100 cal. 100 gm. of water 60C.° = 100 X 1 X 60 = 6000 cal..*. Quantity of heat gained = 6000 calories. 138 MEASUREMENT OF HEAT Sec. 111:21 In the British system, the unit of quantity of heat is the British Thermal Unit. One B.T.U. is the quantity of heat gained or lost when the temperature of one pound of water rises or falls one Fahrenheit degree. Example How many B.T.U. are lost when 100 pounds of water cool from 170°F. to 100°F.? The change in temperature 170 — 100 = 70F.° Quantity of heat lost by: 1 lb. of water cooling 100 lb. of water cooling 100 lb. of water cooling 70F.° = 100 X 1 X 70 = 7000 B.T.U. 1F.°
= 1 B.T.U. 1F.° = 100 X 1 = 100 B.T.U. I j 1 1 Quantity of heat lost = 7000 B.T.U. Note 1. The calorie used when measuring the energy content of foods and fuels (sometimes called the kilogram calorie), is equivalent to 1000 of the calories above. 2. 1 B.T.U. is equivalent to 252 calories. Ill : 21 SPECIFIC HEAT To find the quantity of heat gained or lost by a substance other than water, we must take into account the nature of the substance as well as its mass and the change in its temperature. The calculation is done by multiplying the mass by the change in temperature by a quantity, related to the nature of the substance, called the specific heat. The specific heat of a substance is a number representing the quantity of heat gained or lost by a unit mass of substance when its temperature rises or falls one degree. In the metric system, this is the number of calories of heat gained or lost when the temperature of one gram of the substance rises or falls one centigrade degree. is the number In the British system, it of B.T.U. gained or lost when the temperature of one pound of the substance rises or falls one Fahrenheit degree. The Specific Heats of Some Common Substances Substance Specific Heat Substance Specific Heat Water Alcohol Ice Steam Aluminum 1.000 0.548 0.500 0.500 0.214 Iron Copper Silver Mercury Lead 0.110 0.092 0.056 0.033 0.031 139 : : Chap. 14 HEAT Example 1 How much heat is gained by 50 gm. of mercury when its temperature rises from 20°G. to 60°C.? Solution 1 Change in temperature = 60 — 20 = 40C.°. Quantity of heat required to raise the temperature of 1C.° =.033 cal. 1 gm. of mercury 1C.° =.033 X 50 cal. 50 gm. of mercury 50 gm. of mercury 40C.° =.033 X 50 X 40 = 66 cal. Quantity of heat gained = 66 calories. Solution 2 Change in temperature = 60 — 20 = 40C.° Quantity of heat gained = mass X change in temperature X specific heat = 50 X 40 X.033 = 66 cal. Quantity of heat gained = 66 calories. How much heat is lost by a piece of iron weighing 10 lb. when it cools from 150°F. to
70°F.? Example 2 Solution 1 Change in temperature = 150 — 70 = 80F.° Quantity of heat lost by 1 lb. of iron in cooling 1F.° =.110 B.T.U. 1F.° =.110 X 10 B.T.U. 10 lb. of iron in cooling 10 lb. of iron in cooling 80F.° =.1 10 X 10 X 80 = 88 B.T.U. Quantity of heat lost = 88 B.T.U. Solution 2 Change in temperature = 150 — 70 = 80F.° Quantity of heat lost = mass X change in temperature X specific heat = 10 X 80 X.110 = 88 B.T.U. Quantity of heat lost = 88 B.T.U. 111:22 THE PRINCIPLE OF HEAT EXCHANGE IN MIXTURES As was explained in Sec. 111:19, whenever two substances different temperatures are mixed or in contact, heat passes from the warm one to the cool one until both have attained the at same temperature. Because heat is a form of energy and energy can neither be created nor destroyed (Sec. HI: 3), it follows that the quantity of heat lost by the warm body equals the quantity of heat gained by the cool one. This is the principle of heat exchange. Example 1 A piece of lead weighing 200 gm. and at a temperature of 100°C. is placed in water and the final temperature of the mixture is 25 °C. How much heat is transferred to the water!* 140 MEASUREMENT OF HEAT Sec. 111:22 M = 200 gm. Lead Change in temperature 100 - 25 = 75C.° 100°G. 25°G. Water Quantity of heat lost by the lead = mass X change in temperature X specific heat 200 X 75 X.031 = 465 cal. Heat lost by the lead = gained by the water.. Quantity of heat gained by the water = 465 cal. ‘. Example 2 A mass of 200 gm. of mercury at 100°C. is mixed with an unknown mass of water at 20° C. and the final temperature is 25 °C. Find the mass of the water used. Mercury M = 200 gm. S =.033 Change in temperature = 100 — 25 = 75C.° 100°C. 25°G. 20°C. Quantity of heat lost by the mercury = mass X change in temperature X specific heat = 200 X 75
gm. and a specific heat of.22. If the final temperature is 23 °C., find the mass of the water. Mercury Water Calorimeter Quantity of heat lost by the mercury =: mass X change in temperature X specific heat = 200 X 90 X.033 = 594 cal. Quantity of heat gained by the water = mass X change in temperature X specific heat = V X 5 X 1 = 5.V cal. Quantity of heat gained by the calorimeter = mass X change in temperature X specific heat = 100 X 5 X.22 = no cal. Heat lost by the mercury = heat gained by the water + heat gained by the calorimeter. 5v + 110 594 5v = 594 — no = 484 X = 96.8 Mass of water required = 97 gm. 143 Chap. 14 HEAT Another form of calorimeter, the bomb calorimeter (Fig. 14:3) is used in the determination of the energy content of foods and fuels. Some typical results follow: Calorific Values of Some Common Fuels Fuel B.T.U. per lb. Fuel B.T.U. per cu. ft. Gasoline Fuel Oil Alcohol Soft Goal Hard Goal Wood (average) 20,750 18,500 11,600 14,000 11,600 5,000 III : 24 FINDING THE SPECIFIC HEAT OF A METAL The method generally employed is known as the method of mixtures. The substance whose specific heat is to be determined, say a metal, is mixed with a material which absorbs its heat, say water. From the various observations within the calorimeter the specific heat of the metal can be calculated. A brief summary of the method and a model the Full solution follow. details of Propane Acetylene Natural Gas Goal Gas 2,450 1,450 1,000 300 method are to be found in experiment 7, chapter 15. is A known mass of copper shot heated to a known temperature in a water boiler (Fig. 15:5). The metal is transferred to a certain mass of water at a known temperature contained in the inner vessel of a calorimeter. The mass and specific heat of the calorimeter are known. The mixture is stirred until the highest constant temperature is obtained. A table of data and a model calculation follow. = 100 gm. = 200 gm. Mass of the calorimeter vessel Mass of the vessel and water Mass of the water = 200 — 100 Mass
of the copper shot 100 gm. = 200 gm. = 95 °G. Initial temperature of the copper Initial temperature of the water and vessel = 15°C. Specific heat of the water Specific heat of the calorimeter Final temperature of the mixture Let the specific heat of the copper = 1 =.22 = 25.5°C. = x 144 MEASUREMENT OF HEAT Sec. 111:25 Change in temperature zi: 95 - 25.5 = 69.5C.° Quantity of heat lost by the copper = 200 X 69.5 X X = 13900x cal. Copper M = 200 gm. S = a: 95°C. Water Change in temperature = 25.5 - 15 — 10.5C.° Quantity of heat gained = 100 X 10.5 X 1 = 1050 cal. Quantity of heat gained by the calorimeter = 100 X 10.5 X.22 z= 231 cal. Heat lost by the copper = heat gained by the water + heat gained by the calorimeter. 13900x = 1050 + 231 = 1281 1281 X =— =.092 13900 the specific heat of the copper shot =.092 As in all experiments, some error is unavoidable. Some heat, not accounted for in our method, will be absorbed by other parts of the calorimeter, by the thermometer and a small amount will escape by the methods of heat transfer. With care these losses are quite small. Ill : 25 APPLICATIONS OF SPECIFIC HEAT Specific heats affect our lives more than we realize. Water has the highest specific heat of all common substances Substances with a low (Sec. 111:21). specific heat undergo a great rise in temperature when a given quantity of heat is absorbed. When cooled, those same substances undergo a large drop in temperature. On the other hand, water gains or loses a great quantity of heat without much change in temperature. The high specific heat of water makes it useful in the cooling system of an engine and in automobile hot-water In each case it absorbs large heating. quantities of heat and carries it to a 145 Chap. 14 HEAT radiator to be dissipated. Because it has a higher specific heat than land, water does not reach as high a temperature during the summer season or during the day. In the winter season, or at night, water will not cool to as low a temperature as land for the same reason. Thus temperatures over water or near it will always be more moderate
than inland. For example the Niagara region has a more moderate climate because of the water round it. The Prairie Provinces, on the other hand, will experience extremes of temperature since there are no moderating influences. The daily differences in temperature referred to above are also responsible for land- and sea-breezes (Sec. 111:14) in coastal reAgriculturalists know well that gions. wet soils do not warm as rapidly in because this high spring specific heat of water. Dry, sandy soils warm up more quickly, produce crops earlier and frequently yield more than one crop in a season. dry, of as Metals, as a rule, have low specific 111:21), and this makes heats them ideal for cooking utensils. (Sec. Ill : 26 HEAT EXCHANGE DURING CHANGES OF STATE gases, states three either physical intermediate in All matter is found in the solid, liquid or gaseous state. These are the of matter. Each state of matter consists of moving molecules separated from each other by spaces that vary with the state, largest liquids and in smallest in solids. The rate of motion of the molecules is faster, and the amount of space between them larger, at higher temperatures. Each state may be converted into one of the others by the addition or removal of heat. In solids and liquids, there is a force of attraction between the molecules known as the force of cohesion which must be overcome by the absorption of heat energy before a liquid or gas state may result. Fig. 14:4 shows these changes in state diagrammatically. The heat exchange during melting (fusion) can be illustrated by stirring some chopped ice or snow with a thermometer while warming it very gently over a low flame. The temperature is 0°C. when we begin and does not rise Heat Added Fig. 14:4 Changes of State. 146 MEASUREMENT OF HEAT Sec. 111:26 a wide range of temperature. We should realize also that freezing occurs at the same temperature as melting and that the same quantity of heat is released during freezing as was absorbed during melting. Moreover, when the temperature of a mass of substance is kept at its freezing-point without any change in the quantity of heat, melting and freezing are both occurring at the same rate, i.e., equilibrium will exist between the ice and the water. It is only when heat is added or removed that one or other process predominates. To illustrate heat exchange during boiling, let us heat a
quantity of water from 0°G. to 100°C., stirring constantly with a thermometer. It is found that the temperature does not rise above 100°C., although heat is being absorbed continually. The heat is being used to overcome the force of cohesion rather than the but, since until all the ice has melted. Heat is being temperature absorbed, does not rise, the heat is being used to melt the ice, that is, to overcome the force of cohesion between the molecules. The temperature at which the solid becomes a melting-point. Some substances, ice, sulphur or like salt, have a definite melting-point, while others, like glass, wax and tar, melt over liquid the is Pressure (a) High Pressure Raises Boiling Point. The Pressure Cooker. (b) Low Pressure Lowers Boiling Point. A Commercial Evaporator. (c) Graph Relating Pressure and Boiling Point. Fig. 14:5 The Effect of Changes of Pressure on the Boiling Point of Water. 147 Chap. 14 HEAT and to raise the temperature. The temperaat which the water is changing ture from liquid to vapour throughout the whole mass is called the boiling-point. evaporation Boiling distinguished by the fact that vapour forms throughout the body of the liquid in the former while occurring only at the Because boilingsurface in the latter. points vary with the atmospheric presthey are expressed sure with relation to standard atmospheric 14:5), (Fig. are (760 mm. of mercury). pressure It should be recognized that the boilingpoint is the same as the temperature at which condensation occurs, and the quantity of heat released when a unit mass of vapour condenses is the same as that absorbed during vaporization. Moreover, if the temperature of a mass of liquid is kept at the boiling-point with no change in heat, vaporization and condensation take place simultaneously at i.e., equilibrium exists between liquid and It is only when a change in vapour. the quantity of heat occurs that either process predominates. the same rate, quantity of the Ill : 27 DETERMINING THE HEAT OF FUSION OF ICE In the melting of ice, the quantity of heat required to convert a unit mass to water without a change in of ice temperature is called the heat of fusion of ice. In the metric system, the heat of fusion of ice is the quantity of heat in calories required to change one gram of ice at 0°C. to water at
0°C. To determine it, the method of mixtures is employed again. A brief summary of the method, a set of typical results and a sample calculation are presented below but the method in detail will be found in experiment 8, chapter 15. Small pieces of ice that have been dried with a cloth are allowed to melt with continuous stirring in a known mass of warm water of known temperature, contained in the weighed inner vessel of a calorimeter of known specific heat. When the ice is completely melted, the final temperature is recorded, and, after weighing the vessel and contents, the quantity of ice used may be calculated. Example = 1 00 gm. Mass of calorimeter vessel = 500 gm. Mass of calorimeter and warm water Mass of calorimeter, warm water and melted ice = 592 gm. Mass of warm water = 500 — 100 = 400 gm. Mass of ice used = 592 — 500 = 92 gm. = 32 °C. Initial temperature of water and vessel = 12°C. =.22 = 1 = x Final temperature of water and vessel Let the heat of fusion of ice Specific heat of water * Specific heat of the vessel Before we attempt the calculation, let us examine the heat exchange that occurs. Since the water and the vessel cooled they lost heat. This heat did two things. First it melted the ice at 0°C. to water at 0°C. and then it warmed this water to 12°C. 148 MEASUREMENT OF HEAT Sec. 111:27 Quantity of heat lost by the water = 400 X 20 X 1 = 8000 cal. Quantity of heat lost by the calorimeter = 100 X 20 X.22 = 440 cal. Ice Water M = 92 gm. Heat of F M = 92 gm. S= 1 No change in temperature Quantity of heat gained by the ice melting = 92 X X = 92^: cal. Quantity of heat gained Change in temperature by the ice water warming = 12 - 0 = 12C.° = 92 X 12 X 1 = 1104 cal. Heat lost by the water + heat lost by the calorimeter = heat gained by the ice + heat gained by the ice-water. 8000 + 440 = 92x +1104 92^ = 8000 + 440- 1104 = 7336 92 the heat of fusion of ice = 79.7 cal. There is bound to be a small error in this experiment owing to the use of ice that was not entirely dry
and to heat released by the thermometer and other parts of the equipment. With care a fairly accurate result may be obtained. The accepted value for the heat of fusion of ice is 80 calories per gram. In the British system, the heat of fusion of ice is 144 B.T.U. per pound. It is the quantity of heat required to change a pound of ice at 32°F. to water at 32°F. 149 Chap. 14 HEAT Some Typical Heats of Fusion and Melting-Points Substance M.-P. rc.) H. of F. ( Cal. per gm.) Ice Aluminum Copper 0 660 1083 80 77 42 Substance Lead Cast Iron Mercury M.-P. (^C.) 327 1230 -39 H. of F. ( Cal. per gm.) 6 5.5 3 III : 28 THE IMPORTANCE OF THE HEAT OF FUSION OF ICE When one gram of ice melts without a change in temperature, 80 calories of heat are absorbed. This is enough heat to raise the temperature of one gram of water at 20°C. to the boiling-point, or of 80 grams of water through one centigrade degree. Since such a large quantity of heat is required to melt ice, it is not difficult to understand why ice is useful in preserving food. There are important consequences of this large heat of fusion in nature. Icebergs float long distances before absorbing enough heat to melt. Large snowfalls melt slowly and disastrous floods are avoided. Since ice on lakes and streams melts slowly in spring, sudden extreme changes in temperature do not occur. On the other hand, the heat released when water freezes is useful. Tubs of water are set near fruits and vegetables in unheated basements when there is a chance of frost damage. As the temperature drops, the water freezes and the heat released prevents the fruits from freezing. The heat released when lakes and rivers freeze has a moderating effect and prevents extremes of temperature. This helps to make the climate of regions like Southern Ontario milder than regions more distant from large bodies of Furthermore, the weather genwater. erally becomes milder before or during a snowstorm because of the heat released when the water vapour changes to solid. 150 These examples and many more may be cited to show the usefulness of the heat of fusion of ice. Ill : 29 DETERMINING THE HEAT OF VAPORIZATION OF WATER the called In boiling water, the quantity of heat required to convert a unit
mass of water at its boiling-point to steam without a change in temperature is heat of vaporization of water. In the metric system, the heat of vaporization is the quantity of heat required to change one gram of water at 100°C. to steam at 100°G. (atmospheric pressure being 760 mm. of mercury). Experiment 9, chapter 15, describes the method used to determine it. A brief summary of the method, some typical results and a set of calculations follow. required of heat The quantity to vaporize a unit mass of water at its boiling-point is the same as that released when a unit mass of steam condenses. Since the latter is more easily determined, the method involves using it rather than the former. Hence, steam from a boiler is passed through a steam trap to free it of water (It is now called “dry” or “live” steam). It is then conducted into a quantity of cool water of known mass and temperature contained in the weighed inner vessel of a calorimeter of known specific (Fig. 14:6). The water is continually stirred and, shortly, the final temperature is recorded. The vessel and contents are weighed to find out the weight of steam used. heat MEASUREMENT OF HEAT Sec. 111:29 Mass of inner vessel of calorimeter = 100 gm. = 500 gm. Mass of vessel and cool water Mass of vessel, water and condensed steam = 521.7 gm, Mass of cool water = 500 — 100 = 400 gm. = 521.7 — 500 = 21.7 gm. Mass of steam = 5°C. Initial temperature of water and vessel = 36°C. =.22 = 1 = X Let the heat of vaporization of water Specific heat of the vessel Specific heat of water Final temperature Let us analyse these results before proceeding. The heat absorbed by the water and the vessel originated not only from the condensation of the steam, but also from the cooling of the resulting water from 100°C. to 36°C. We must recognize these two sources of heat in our calculations. Steam Water formed by condensa- tion Cool Water Calorimeter M = 21.7 gm. HofV M = 21.7 gm. S = 1 No change in temperature Quantity of heat lost by the steam condensing = 21.7 X x^2\Jx cal. Change in temperature = 100 — 36 = 64C.° Quantity of
heat lost by the resulting water cool- ing = 21.7 X 64 X 1 = 1389 cal. 100°C. 36°G. 5'^C. M = 400 gm. S = 1 M = 100 gm. S =.22 Change in temperature = 36 — 5 = 31C.° Quantity of heat gained by the cool water = 400 X 31 X 1 = 12400 cal. Quantity of heat gained by the calorimeter = 100 X 31 X.22 = 682 cal. 151 Chap. 14 HEAT The heat lost by the steam + heat lost by the resulting water = the heat gained by the cool water + heat gained by the calorimeter. 21.7a: + 1389 = 12400 + 682 21.7a: = 12400 + 682 — 1389 = 11693 11693 ^ =— = 538.8.’. the calculated heat of vaporization of water is 539 calories. The accepted value is 540 calories. In the British system, the heat of vaporization of water is 972 B.T.U. per pound and is the quantity of heat required to change a pound of water at 212°F. to steam at 212°F. Heats of Vaporization and Boiling-Points of Various Useful Materials Substance Water Ethyl Alcohol Ethyl Ether Chloroform Ammonia Methyl Chloride Sulphur Dioxidfe Freon 12 B.-P. rc.) 100 78 35 61 — 33 — 24 — 10 — 30 H. of V. ( Cal. per gm.) 540 204 84 59 327 102 95 41 III : 30 APPLICATIONS OF HEAT OF VAPORIZATION (a) Water of heat The high vaporization of water is of great practical importance in nature. Evaporation of soil water is slow because of the vast quantity of heat required for this purpose. Thus extremes of drought and torrential that would attend excessive evaporation are avoided. rains Steam-heating, as used in most large ex- is an excellent buildings, public 152 Fig. 14:6 Determining the Heat of Vaporization of Water. ample of heat of vaporization at work. Water is boiled; the steam is conducted to radiators where it condenses and yields its heat of vaporization. The hot water now flows back to the boiler to be used again. This system is cheaper than hotwater heating (Sec. 111:14) as smaller radiators are required and
vel (Canada) Ltd. Fig. 14:9 The Operation of a Gas Refrigerator. quick-freeze units etc., all work on the same principle. (c) The Liquefaction of Gases learn more later Michael Faraday, about whom we (Sec. V:57), shall devised an ingenious method of liquefying gases. He filled a thick-walled glass tube of the type shown in Fig. 14:10 with chlorine gas. One end of the tube was surrounded by a freezing mixture of Fig. 14:10 (a) Illustrating Faraday's Method of Liquefying Gases, (b) Producing Cold Artificially. 154 MEASUREMENT OF HEAT Sec. Ill: 30 ice and salt. Heating the gas in the other end caused a rise in pressure while the gas liquefied in the cool end. In this way he was also able to liquefy several other gases. This principle is employed in the gas refrigerator above. methyl chloride and freon 12 are said to be easily liquefied at ordinary tem- peratures. When a compressed gas is allowed As an exto expand, cooling results. ample, the air escaping from an inflated oxygen, hydrogen, Faraday found that certain gases, for example, nitrogen, air and many others, could not be liquefied in this way. It was found that these gases had to be cooled to a certain temperature, called the critical temperabefore any amount of pressure ture, would liquefy them. The pressure required to liquefy the gas at this temperature is known as the critical pressure. It should be noted that when the operating temperature is lower than the critical temperature, the quired for liquefaction pressure reis very much lower than the critical pressure. not difficult to understand, then, why dioxide, ammonia. the sulphur gases It is Some Critical Temperatures AND Pressures Substance C.T. C.P. (°C.) (Atm.-^) 78 132 143 112 157 144 76 66 112 40 Sulphur Dioxide Chlorine Methyl Chloride Ammonia Freon 12 Carbon Dioxide Oxygen Air Nitrogen Hydrogen Helium *One atmosphere pressure = 760 m.m of mercury. - 119 — 141 — 147 - 240 - 268 73 50 34 37 13 31 2 ABC High Pressure D E F Low Pressure Fig. 14:11 The Production of Liquid Air. 155 Chap. 14 HEAT automobile tire feels cold. In
14:13 The Steam Turbine. (a) Principle of the Steam Turbine. This type of steam-engine is widely used in power-plants and large ships. 14:13). The force of the vapour rotates the paddle-wheel. are These engines 157 @ CONT«Ot «O0M (?) STATION SERVICE TRANSfORMER © ELECTRIC' GENERATOR © CONDENSER ©TURBINE ©BOOSTER PUMP © FEED PUMP ©STEAM GENERATOR CONTROL ©CONDENSATE PUMP ©STATION SERVICE SWITCHBOARD @ HEATERS ©COAL FEEDER @ TRIPPER © SCALES @ PULVERIZER © STEAM-GENERATOR @ COAL CONVEYOR © STEAM LINE © FORCED DRAFT FAN © AIR INTAKE ® IN OUCED DRAFT FAN ® MECHANICAL OUST COLLECTOR ® ELECTROSTATIC PRECIPITATOR © CRANE Fig. 14:13 (b) How a Steam Generating Station Works. Ontario Hydro Richard L. Hearn Generating Station. Ontario Hydro 158 MEASUREMENT OF HEAT Sec. 111:31 Fig. 14:14 The Four Cycle Internal Combustion Engine. A Sectional View. possible. designed to use the pressure as efficiently They run at very high as speeds and are more efficient and smaller than ordinary steam-engines of the same capacity. The Internal-Combustion Engine If a compact, powerful, mobile source of power is required, the internal-com- bustion engine is the choice. This type of engine can be adapted to the use of any fuel that can be vaporized, such as Coal gasoline, gas is used in some engines, while the Diesel type employs cheap petroleum alcohol, and kerosene. oils. The Gasoline Engine The type generally used is the fourcycle engine, so named because the piston makes four strokes for each explosion of gas in the cylinder. Once started it will run automatically as long as the three necessities of fuel, compression and spark are met. Smoothness of operation is accomplished by the use of a heavy flywheel and of several cylinders which fire Students will have at different times. understanding engine after studying Fig. 14:14. Further treatment than this is beyond the scope of this text. difficulty little this in Chrysler Corporation A Cut-Away Photograph of a Modern Internal Combustion Engine. The
Diesel Engine This engine operates like a four-stroke gasoline engine but is without carburetor or electrical ignition system. Air is 159 Chap. 14 HEAT to about one-sixteenth of forced into the cylinder and is compressed its volume and for that reason becomes hot. When oil is forced into this hot gas, it burns, without any need for a spark. The Jet Engine The last few years have seen the very rapid development of a new type of internal combustion engine, the Jet Engine. There are several types of such engines; the commonest, however, is the TurboJet. Air is scooped into the intake at the front of the engine. It is compressed, and consequently heated, by a compressor. This heated air is driven under high pressure into the combustion chamber where fuel is injected in and combustion occurs. The hot expanding gases stream away at a high velocity. A small portion of their energy is used to drive the turbine Most which operates the compressor. of the energy is in the stream of hot gases which is ejected from the rear of the engine. The force exerted by this jet creates an equal of hot gases (action) and opposite force (reaction) that drives the plane forward. Rockets are another type of modern reaction engine that operate very similarly to the jet engine described above. They differ in that they carry their own supply of oxygen to burn the fuel. As a result rockets can travel through outer space where there is no air. Inter-planetary travel, a thing long dreamed about, now seems to be becoming a real pos- sibility. III : 32 QUESTIONS A 1. (a) Distinguish between quantity of heat and temperature. (b) State the factors that govern the quantity of heat possessed by a body. 2. (a) Define: calorie, British Thermal Unit, specific heat. (b) What quantity of heat is needed to: (i) warm 25 gm. of water from 13°C. to 27°C.? (ii) heat 37 lb. of water from 68°F. to 212°F.? 3. of 25 copper 22°C. gm. from (iii) heat (S.H. =.092) 100°C.? (a) What is the exchange in mixtures? (b) How long does heat exchange continue between two substances in principle of heat to contact? (c) What is the purpose of a calorimeter? How does it fulfil its purpose? 160 4. (a) Describe an
experiment to find the specific heat of a metal. (b) When a 200 gm. mass of metal at a temperature of 85°C. is immersed in 300 gm. of water at 30°C., the final temperature is 33°C. Calculate the specific heat of the metal. 5. (a) Distinguish between boiling and evaporation. (b) Define melting-point and boiling- point. 6. (a) Define heat of fusion of ice and state its numerical value in the metric and British systems. 7. (b) Describe how you would determine its value experimentally. (a) How much heat will be released when 50 gm. of water at 0°C. freeze to Ice at 0°C.? (b) How much heat will be absorbed in the melting of 20 gm. of ice at 0°C. to water at 0°C.? (c) How much heat will be required MEASUREMENT OF HEAT Sec. 111:32 to convert 80 gm. of ice at 0°C. to water at 25°C.? 8. (a) Define heat of vaporization of 9. 10. that from water. (b) Why is a burn from steam much more severe hot than water? (a) How much heat will be required to convert 50 gm. of water at 1 00°C. to steam at 1 00°C.? (b) How much heat will be released when 1 5 gm. of steam at 1 00°C. are condensed to water at 100°C.? (c) How much heat will be released when 35 gm. of steam at 100°C. are condensed to water and the water is cooled to 20°C.? 8. When 25 gm. of water at 100°C. are added to 50 gms. of water at 10°C., what is the final temperature? 9. When 200 gm. of metal at 100°C. are placed in 200 gm. of water at 1 5.0°C., final temperature becomes 23.0°C. the Calculate the specific heat of the metal. 10. A brass kilogram weight at a tem- of 90.0°C. is submerged perature in 440 gm. of water at 10.0°C. The final temperature is 24.0°C. Find the specific heat of the brass. 11. 49 gm. of water at
1 3°C. are contained in an aluminum calorimeter weighing 50 gm. If 35 gm. of glass at 87°C. are dropped Into the calorimeter the temperature becomes 21°C. Find the specific heat (a) Explain the principle of operation of the glass. of the electric refrigerator. (b) How is air liquefied? B 1. How much heat is required to raise the temperature of 2 kg. of water from 25°C. to 75°C.? 2. How many B.T.U. will be absorbed when 30 gallons of water in a hot-water tank are heated from 70°F. to 200°F.? (1 gallon of water weighs 10 lb.) 3. How much heat is lost when 1.3 kg. of water are cooled from 90°C. to 20°C.? 4. How much heat in will be released when 15 gallons of water cool from 1 65°F. to 1 25°F.? B.T.U. 5. How many calories of heat must be supplied to heat 200 gm. of cast iron from 20.0°C. to 80.0°C.? 6. How much heat does a silver spoon weighing 30.0 gm. absorb when placed in a cup of coffee that raises its temperature from 20.0°C. to 80.0°C.? 7. How many grams of water at 85. 0°C. must be added to 100 gm. of water at 10.0°C. to give a final temperature of 37.0°C.? 12. In an experiment, 500 gm. of lead at 100°C. are placed in 100 gm. of water at 14°C. contained in a copper calorimeter weighing 80 gm. The final temperature is 25°C. Find the specific heat of the lead. 13. What mass of iron at 90.0°C. when added to 200 gm. of water at 1 5.0°C. contained in a copper calorimeter weighing 100 gm. will give a final temperature of 25.0°C.? 14. When 400 gm. of silver at 100°C. was placed in water at 1 6.0°C. contained in an aluminum calorimeter weighing 40.0 gm. the final temperature was 24.0°C. What mass of water was used? 15. Calculate the final temperature when 120 gm. of iron at
100°C. are added to 400 gm. of water at 10°C. in a copper calorimeter having a mass of 80 gm. 16. A copper calorimeter weighing 65 gm. contains 30 gm. of turpentine at 15°C. When 45 gm. of Iron at 98°C. are placed temperature becomes 32°C. Calculate the specific heat of the turpentine. 17. How much ice af 0°C. can be melted the it, in by 1 kg. of water at 100°C.? 18. How much ice at 0°C. will be required 161 Chap. 14 HEAT to cool 1 kg. of drinking-water from 15°C. to 0°C.? ture is 27°C. Find the heat of vaporization of water. 19. What mass of ice at 0°C. will be required to cool 750 gm. of water from 35°C to 10°C? 20. When 5,0 gm. of ice at 0°C. are melted in 30 gm. of water at 25°C. the final temperature is 10°C. Find the heat of fusion. 21. A copper calorimeter weighing 55 gm. contains 90 gm. of water at 25°C. When 15 gm. of ice at 0°C. are melted in the water the resulting temperature is 1 1 °C. Find the heat of fusion of ice. 22. In an experiment 203 gm. of water at 40°C. are contained in a calorimeter vessel weighing 50 gm. having a specific heat of.22. After ice at 0°C. was melted in the water the temperature became 25°C. and the mass 233 gm. Find the heat of fusion of ice. If 15 gm. of ice at — 20°C. are 23. melted in 50 gm. of water at 40°C. and the resulting temperature is 10°C., cal- culate the specific heat of ice. 24. How many grams of water can be freezing-point raised boilingpoint by the condensation of 5.0 gm. of steam? from to 25. To what temperature will 75 gm. of water at 25°C. be heated by the condensation of 3.0 gm. of steam? 26. When 6.6 gm. of steam at 1 00°C. are passed into 1 80 gm
. of water at 6.0°C. contained calorimeter weighing 45 gm., the resulting tempera- aluminum an in 27. If 15 gm. of steam at 100°C. are added to 150 gm. of water at 20°C. in a calorimeter (S.H. = 0.10) weighing 75 gm. the final temperature is 74°C. Calculate the heat of vaporization of water. 28. When 160 gm. of water at 7.7°C., contained in an aluminum calorimeter weigh1 26.2 gm., are heated by the condensation of 10.1 gm. of steam, the final temperature is 39.8°C. Find the heat of vaporization of water. ing the Find final 29. Find the resultant temperature when 8.0 gm. of steam at 100°C. are passed into a vessel of negligible mass containing 40 gm. of ice at 0°C. 30. temperature when 20 gm. of steam at 1 00°C. are passed into 240 gm. of water at 10°C. contained in an aluminum calorimeter weighing 150 gm. 31. What quantity of heat will convert at — 1 6°C. to steam at 5 gm. of ice 100°C.? 32. When 45.0 gm. of iron at 95.0°C. are placed in a cavity in a block of ice at 0°C. and the temperature has dropped to 0°C., 6.0 gm. of ice are melted. Knowing the heat of fusion of ice, find the specific heat of iron. 33. An ice-water mixture weighing 200 gm. is contained in a calorimeter weighing 100 gm. (S.H. = 0.20). When 35 gm. of steam at 100°C. are added the temperature becomes 50°C. Calculate the mass of ice used. 162 CHAPTER 15 EXPERIMENTS IN HEAT INTRODUCTION Before commencing these experiments in heat, students should be familiar with the following. A. The Use of the Bunsen Burner 1. Structure of the Burner Examine a Bunsen burner and identify the gas inlet, the orifice, the air-inlet valve, the mixing tube. Make a labelled diagram of the burner. 2. Lighting the Burner (a) Close the air inlet, turn on the gas and ignite it
. Gradually open the air inlet until you have the desired flame. If the flame “strikes back”, i.e., burns at the bottom of the (b) mixing tube, turn off the gas and repeat (a) above. 163 Chap. 15 HEAT 3. Regulating the Size and Temperature (Colour) of the Flame (a) The size of the flame may be changed by increasing or decreasing the supply of gas. (b) When first low for most purposes. When the air inlet is gradually opened, the colour changes from yellow, through blue to nearly colourless, and the temperature increases until it is a maximum at the last stage. lit, the flame is yellow and its temperature is too 4. The Structure of the Flame Fig. 15:2 shows the various regions (cones) of a Bunsen flame. An object to be heated is held just above the turquoise cone. B. The Use of the Thermometer 1. Examine the instrument and find the centigrade scale. (Some ther- mometers have centigrade and Fahrenheit scales.) 2. Wait until the liquid has come to rest before taking a reading. 3. Adjust the thermometer so that you are able to view the top surface of the liquid at right angles in order to avoid the error of parallax. 4. Take readings to a fraction of a degree. EXPERIMENT 1 To study the expansion of solids, (Ref. Sec. III:5) Apparatus Bunsen burner, ball-and-ring apparatus, cold water. Method 1. Try to pass the ball through the ring when both are cold. 164 EXPERIMENTS IN HEAT 2. Heat the ball strongly and try to pass the ball through the ring again. 3. Cool the ball by placing it in cold water and again try to pass it through the ring. Observations What do you observe in the above steps? Conclusion What is the effect of heating and cooling on the volume of a solid? Questions 1. What would be the probable effect of heating the ring and trying to pass the heated ball through it? 2. What would be the probable effect of chilling the ring in a freezing mixture and trying to pass the ball through it? 3. By means of labelled diagrams, show how you would demonstrate the effect of heating and cooling on the volume of (a) a liquid, (b) a gas. EXPERIMENT 2 To compare the expansion of different
metals when heated. (Ref. Sec. Ill: 5) Apparatus Bunsen burner, compound bar consisting of strips of copper and iron fastened together, cold water. Method 1. Heat the long straight compound bar in the Bunsen-burner flame and note any change. 2. Cool the bar in cold water and again note the change. Observations 1. Describe the changes that occurred in parts 1 and 2. 2. Which metal was on the outside of the curve? Explanation Account for the changes. Conclusion What is the relative amount of expansion and contraction that occurs when different metals undergo the same change in temperature? Question Make a labelled diagram to show how to use a compound bar as a thermostat to control an oil burner and thus regulate the temperature in a room. 165 Chap. 15 HEAT EXPERIMENT 3 To study the transfer of heat by conduction. (Ref. Sec. 111:13) Apparatus Bunsen burner, metal rod about 12 in. long with a wooden handle, a conductometer (Fig. 13:1), wax. Method 1. Place drops of wax at three-inch intervals along the length of the long metal rod. Hold it by the wooden handle and heat the end of the rod strongly in the flame of the burner. 2. Place drops of wax at equal intervals along the rods of the conductometer and heat the metals simultaneously at the point where the rods meet. Observations 1. (a) What happens to the wax in part 1? (b) Is there any change noted in the temperature of the wooden handle? 2. State the differences observed in each metal rod in part 2. Conclusions 1. State the meaning of the term conduction of heat. Explain how it occurs. 2. What have we learned about the heat conductivity of different metals? How does wood compare with metals in this regard? 3. List the metals studied in order of their relative heat conductivities. Questions 1. How do metals compare with other substances in heat conductivity? 2. What use is made of the conductivity of heat through metals? 3. Why are liquids and gases very poor conductors of heat? 4. List some materials that are good insulators and state where they are used for this purpose. EXPERIMENT 4 To study the transfer of heat by convection. (Ref. Sec. 111:14) A. IN LIQUIDS Apparatus A large beaker, retort stand, ring, Bunsen burner
, cold water, potassium permanganate. Method Fill the beaker with water and place it on the ring attached to the stand. Make sure that the water is at rest. Drop a crystal of potassium 166 EXPERIMENTS IN HEAT permanganate into the water near the edge. Using the tip of the low Bunsen flame, heat the liquid beneath the crystal. Observations Describe all phenomena. Explanation Account for the changes observed. B. IN GASES Apparatus A candle, smoke-paper, convection apparatus (Fig. 13; 6b). Method Light the candle and place it beneath one of the chimneys. Close the Hold a piece of lighted smoke-paper above the other glass front. chimney. Observations State what occurs. Explanation Account for these results. Conclusion State the meaning of the term convection currents and explain how they occur. Question Show by means of a diagram how heat is transferred from the furnace to an upper room in a home heated by (a) a simple hot- water system (b) a simple hot-air system. EXPERIMENT 5 To compare the abilities of dull/ dark and shiny/ light surfaces to emit radiant energy. (Ref. Sec. Ill; 15(b) Apparatus A differential thermometer with both bulbs blackened with soot from a candle, metal vessel with one side blackened and the other polished, some boiling water. 167 Chap. 15 HEAT Method Mark the levels of the coloured liquid in the arms of the differential thermometer and then place the metal vessel full of boiling water midway between the bulbs. Note any change in the levels of the coloured liquid. Observations What is observed? Explanation Account for your observations. Conclusion What effect has the nature of the surface of an object on its ability to emit radiant energy? Questions 1. Why is this apparatus called a differential thermometer? 2. Why should tea-pots be shiny rather than dull? EXPERIMENT 6 To compare the abilities of dull, dark and shiny, light surfaces to absorb radiant energy. (Ref. Sec. Ill; 15(c) Apparatus A differential thermometer with one bulb shiny and one blackened, dull, dark metal vessel, supply of boiling water. Method Mark the levels of the coloured liquid in the differential thermometer and place the vessel filled with boiling water midway between the two bulbs. Note any changes in the levels of the liquid. Observations What is observed? Explanation Account for the observations. 168
EXPERIMENTS IN HEAT Conclusion What effect has the nature of the surface on its ability to absorb radiant energy? Questions 1. In experiment 5, why were the bulbs of the differential thermometer darkened? 2. In experiment 6, why is a dull, dark vessel used? 3. Why do people wear dark clothing in winter and light-coloured clothes in summer? 4. Examine a radiometer and make a labelled diagram of it. Note and explain what happens when a source of radiant energy is brought near it. EXPERIMENT 7 To determine the specific heat of a metal, (Ref. Sec. 111:24) Apparatus A quantity of copper (or lead) shot, balance and weights, flask, testtube, water, retort stand, ring, gauze, Bunsen burner, calorimeter, two thermometers. Method 1. Fill the test-tube three-quarters full of shot and carefully insert the Place the shot and its container in bulb of a thermometer into it. the flask and boil the water while carrying out parts 2, 3 and 4. Note the temperature of the shot to within a fraction of a degree after the mercury stops rising. 2. Find the mass of the inner vessel of the calorimeter and stirrer. Record the specific heat of the metal of which both are made. 3. Place about 100 ml. of cold tap-water whose temperature is slightly lower than room temperature in the inner vessel. Find the mass of the vessel and water, and determine the mass of the water. 169 Chap. 15 HEAT 4. Place the inner vessel and contents into the outer vessel. Cover with the lid. Stir the water and take its temperature. 5. Open the calorimeter, add the shot to the water, close it, and after stirring the mixture, again take its temperature. 6. Find the mass of the vessel, stirrer, and contents, and determine the mass of the shot. Observations = 1. Temperature of the shot 2. Mass of the inner vessel and stirrer == = 3. Mass of the inner vessel, stirrer and water = 4. Initial temperature of the vessel and water 5. Final temperature of the mixture of water and shot = 6. Mass of the vessel, stirrers and mixture =: = = = Specific heat of the vessel Specific heat of the water Let the specific heat of the shot x Calculations Study the worked example in Sec. 111:24 and calculate the specific heat of the metal from the
observations recorded above. Conclusions 1. What is your experimental value? 2. What is the class average? Questions 1. What is the percentage error? 2. What are the sources of error in this experiment? 3. Why is it desirable to have the initial temperature a few degrees lower than room temperature? EXPERIMENT 8 To determine the heat of fusion of ice. (Ref. Sec. 111:27) Apparatus Quantity of ice, paper towels, thermometer, balance and weights, quantity of water at about 10C.° warmer than room temperature, calorimeter. Method 1. Find the mass of the inner vessel and stirrer. 2. Place about 100 ml. of the warm water in the vessel and again find the mass. 3. Place the inner vessel in the outer one. Cover with the lid. Stir the water and take its temperature, estimating it to a fraction of a degree. 170 EXPERIMENTS IN HEAT 4. Wipe dry about 25 gm. of ice with the paper towels and quickly drop it into the warm water. Replace the cover and stir until the ice has melted completely. Record the lowest temperature reached by the water. 5. Find the mass of the vessel, stirrer, and contents, and determine the mass of the ice. Observations = 1. Mass of inner vessel and stirrer = 2. Mass of inner vessel, stirrer and water 3. Initial temperature of the water and vessel = 4. Final temperature of the mixture of original water and melted ice 5. Mass of vessel, stirrer and the mixture Specific heat of the vessel Specific heat of the water Initial temperature of the ice Let the heat of fusion of ice = =: = = = = x Calculations Study the worked example in Sec. 111:27 and calculate the heat of fusion of ice from the observations recorded above. Conclusions 1. What is the experimental value for the heat of fusion of ice? 2. What is the class average? Questions 1. What is the percentage error? 2. What are the sources of error in this experiment? 3. Why is it desirable to have the initial temperature a few degrees higher than room temperature? 4. Why do we dry the ice before placing it in the water? 171 Chap. 15 HEAT EXPERIMENT 9 To determine the heat of vaporization of water, 111:29) (Ref. Sec. Apparatus A calorimeter, quantity of water at about 15C.° below room temperature, thermometer
, Bunsen burner, retort stand, ring, gauze, steamboiler, steam-trap, rubber connectors (Fig. 14:6). Method Place the boiler containing water on the ring of the retort stand and heat it. 1. Find the mass of the inner vessel and stirrer. 2. Put about 100 ml. of the cold water into the inner vessel and find the combined mass. 3. Place the inner vessel in the outer one and put on the lid. Stir the water and take its temperature, estimating it to a fraction of a degree. 4. Connect the steam-trap with the boiler and conduct steam into the water. Stir constantly until its temperature has risen as much above room temperature as it was originally below it. Discontinue passing steam into the water and take the highest temperature reached by the water. 5. Find the mass of the inner vessel and contents. Observations 1. Mass of inner vessel and stirrer 2. Mass of inner vessel, stirrer and water 3. Initial temperature of the mixture 4. Final temperature of the mixture 5. Mass of vessel, stirrer and mixture Specific heat of the vessel Specific heat of the water Initial temperature of the steam Let the heat of vaporization of water - <2 - X Calculations Study the worked example in Sec. 111:29 and calculate the heat of vaporization of water from the observations recorded above. Conclusions 1. What is the experimental value for the heat of vaporization of water? 2. What is the class average? Questions 1. What is the percentage error? 2. What are the sources of error in this experiment? 3. How may the effect of the sources of error be minimized? 4. Why is it important to use the steam-trap? 172 UNIT IV LIGHT These Searchlights Create an Interesting Construction, Showing both a Converging and a Diverging Pencil of Light Rays. Wheeler Newspaper Syndicate CHAPTER 16 NATURE AND PROPAGATION OF LIGHT IV : 1 NATURE OF LIGHT (sight). Light is that agency which affects the eye and produces the sensation of “seeThat branch of physics ing” that covers all the phenomena pertainlight is called Optics (Greek, ing to ops—eye). Some knowledge of light existed from very early times, though this was limited effects rather than to any fundamental understanding. primarily to As to the nature of light, the early Greeks believed it to consist of streams of minute particles of some sort. There was considerable debate as
to whether these particles originated in the eye or Plato (428-348 in the object viewed. B.G.) and Euclid (about 300 b.c.) held to the idea that invisible feelers were emitted from the eye, and that the eye sees a body somewhat as the hand may feel it with a rod. The Pythagoreans, Aristotle (284-322 b.c.) in particular, opposed this view and taught that light consisted of minute particles projected into the eye from the object. Both these conflicting ideas were mere guesses and as such were worthless. However, in the eleventh century Alhazen, an Arabian evidence physicist, provided definite showing that the cause of vision proceeded from the object and not the eye. Even to-day, much mystery still surrounds the nature of light (Sec. IV; 7). In view of the fact that light can be produced from other forms of energy, e.g., heat energy, and that light can be transformed into other forms of energy, (Sec. V:82), we shall e.g., simply say that light is a form of energy. electricity IV: 2 SOURCES OF LIGHT Few objects give out light and these are termed luminous bodies. Most objects are non-luminous, becoming visible only when they reflect light from some outside source to our eyes (Fig. 16:1). Our main source of light is the sun. When we think how important the sun has always been in human affairs, it not surprising that in prehistoric times it became a prime object of worship. the ancient Egyptian History records Sun-god, Ra, and an ancient Persian god of light, Ahura-mazda. The terms “ray” of light, and “mazda” lamps are derived from these names. is Many objects are rendered luminous by being heated to incandescence. This may be accomplished by mechanical means as shown when sparks are produced by friction between flint and steel in a gas-lighter; by resistance to an electric current in the thin wire used in electric-light bulbs; and by chemical action as in the burning of a fuel. Some objects are luminous at ordinary tem- 175 Chap. 16 LIGHT 16:1 Self-LumFig. inous and Non-Lum- inous Objects. Tigerstedt Studios, Calgary It such as frosted glass or oiled paper, is one that transmits some light, but in doing so distorts
or scatters the light so that we cannot see clearly objects on the other side. Opaque substances, like wood, do not transmit light at all and hence we cannot see through them. is common knowledge that light travels in straight lines. Our inability to see around corners, the formation of shadows, and other examples point to this conclusion. This behaviour of light is termed rectilinear propagation. Knowing this, we represent a path of light by a straight line called a ray. (Note: the light that travels along this path is also called a ray.) The direction in which the light is travelling is indicated by arrow-heads placed on the rays. Several parallel rays form a beam of light. Rays of light proceeding towards a point form a converging pencil; when they spread out from a point they form a diverging pencil (Fig. 16:2). IV: 4 PIN-HOLE CAMERA The pin-hole camera is an interesting of electricity of phosphorus, for peratures, a stick example, and fluorescent bodies. Then there is the glow produced by the discharge certain gases, e.g., neon tubes. Another interesting example of “cold light” is that produced by fireflies, and by certain deepsea fish. Probably such light is produced by chemical means. through IV: 3 TRANSMISSION OF LIGHT fact that light Unlike sound, light does not require a material medium for its transmission. Evidence in support of this is supplied by travels through a the vacuum in coming to us from objects in space, and from the glowing filament of an evacuated tube. Further evidence was provided in experiment 4, chapter 10, where we could not hear the bell when the air was evacuated from the jar yet could still see it ringing. Various media diflfer in their ability to transmit light. Transparent objects such as air, glass and water transmit is easy to see light so readily that it through them. A translucent substance. 176 NATURE AND PROPAGATION OF LIGHT Sec. IV: 4 Glass bricks are used in the many construction modern of buildings. What are the advantages? Canadian Pittsburgh Industries Ltd. application of the rectilinear propagaIt consists of an opaque tion of light. box, having a small hole (pin-hole) in the middle of one end, and a translucent screen (piece of ground glass, or oiled paper) at the other. If a lighted candle is placed a little distance in front of the pin-hole, an inverted image of the candle will be
seen on the translucent screen. \ / / \ (a) Fig. 16:2 Rectilinear Propagation of Light (a) Ray (b) Beam (c) Converging Pencil. (d) Diverging Pencil. 177. Chap. 16 LIGHT however, because of the small amount of light admitted through the pin-hole. IV : 5 SHADOWS AND ECLIPSES A shadow is the dark space behind an opaque object, an area from which light has been partially or completely excluded. An opaque object in front of a point source of light will cut off all the light, and a sharply defined shadow is produced. If the light comes from a larger source, the shadow will vary in intensity, the dark central portion of the shadow which receives no light from any part of the source being the umbra 16:4a), the lighter shadow sur(Fig. rounding the umbra which receives some light being the penumbra (Fig. 16:4b). An eclipse of the sun is an interesting shadow phenomenon caused when the moon comes between the sun and earth 16:5). A person located in the (Fig. moon’s umbra will total If in the moon’s eclipse of the sun. observe a This kind of image is formed as a result of very narrow diverging pencils of light from each point of the object passing through the pin-hole, and producing small patches of light, identical in shape to the pin-hole, on the screen. Fig. 16:3 The Pin-Hole Camera. or The resulting image is formed by a large number of these overlapping patches of light, producing an exact replica of the original object. Such an image is a real image. The image so obtained will have a somewhat blurred, out-of-focus appearance due to the circular edges of each patch of light not entirely overlapping. The larger the pin-hole the brighter will be the image on the screen, but the more blurred will be its edges. The image is inverted because the light rays cross at the pin-hole (Fig. 16:3). The size of the image is governed by the size of the object, its distance from the camera, and the distance of the image from the (Chap. 21, Exp. 1 ) pin-hole Size of Image Distance of Image Size of Object Distance of Object Hi _ Di 1h~1^ A consideration of the equiangular (or similar) triangles formed by the rays of should light
as shown in 16:3 Fig. establish these relationships fairly readily. If we replace the translucent screen with a light-sensitive paper, or photographic plate, quite acceptable photographs of distant objects can be obtained. A very long exposure is necessary, 178 Fig. 16:4 Shadows (a) Using Point Source. (b) Using Large Source. eclipse of the sun. penumbra, he will be able to see part of the sun. The latter is called a parBecause the tial moon’s orbit around the earth is slightly its distance from the earth Thus it occasionally happens elliptical varies. NATURE AND PROPAGATION OF LIGHT Sec. IV: 6 that the moon comes between the sun and the earth at a time when its umbra does not reach the surface of the earth. A person located on the earth below the tip of the moon’s umbra would see a ring of the sun around the edge of the moon. Such an eclipse is called an annular very eclipse sun and occurs the of rarely. Eclipses of the moon also occur, and at fairly frequent intervals. The moon is a non-luminous body, and is seen only when sunlight is reflected from its surface to the earth. The full moon occurs when the moon is on the opposite side of the earth from the sun. At such a time the moon may pass through the earth’s A partial shadow and be eclipse of the moon is caused when it eclipsed. (a) (b) Fig. 16:5 Eclipses. (a) Total and Partial Eclipse of the Sun. (b) Annular Eclipse of the Sun. (c) Eclipse of the Moon. is partly in the earth’s umbra, and a total eclipse when it is completely in the earth’s umbra. When in the earth’s penumbra, the moon is not eclipsed, but only less bright as it receives, and hence reflects, less light from the sun. IV : 6 VELOCITY OF LIGHT It has long been suspected that light travels with a finite velocity, but early attempts to measure this velocity were Fig. 16:6 Velocity of Light Using the Moons of Jupiter. light too crude to be successful. The first reasonably accurate value was obtained by a young Danish astronomer Olaus Romer in 1676. He found that intervals between the successive eclipses of one of the moons of the planet Jupiter were longer when Earth was receding from Jupiter (going from
Ei to E 2 ) and shorter when Earth was approaching (going from Eg to E^, Fig. 16:6). Romer ascribed the discrepancy to the time required for the to diameter of the earth’s orbit. The timelag was found to be about 16.5 minutes or approximately 1000 seconds. Since the diameter of the earth’s orbit is about 186,000,000 miles, the velocity of light is found to be 186,000 miles per second. The first determination of the velocity distances on the of earth was made in 1849 by A. H. Fizeau. His method was to pass a beam of light through one of the gaps in a toothed wheel, and reflect it back on its path from a mirror three or four miles away light over short across travel 179 Chap. 16 LIGHT : (Fig. 16:7). When the wheel was at rest, the return beam passed back through the same gap and was visible on the other side. When the wheel was rotated rapidly, a speed could be found at which Fizeau's ApFig. 16:7 paratus for Measuring Velocity of Scheme of Light. the return way was blocked by the next tooth. The time spent by the wheel in spinning through this small part of a revolution, is also the time required for the light to travel to the distant mirror and back again. Hence, knowing these facts, the velocity of light could be easily calculated. A better method was devised by J. L. Foucault in 1850, who used a rotating mirror instead of a toothed wheel. This method was used in more elaborate form by A. A. Michelson in 1926, with an eight-sided mirror and a considerably increased light path (Fig. 16:8). More recently, Michelson in collaboration with others, set up a mile-long evacuated tube with a mirror arrangement for causing a beam of light to traverse this path back and forth many times before being obAgain using a rotating-mirror served. method, they obtained a quite accurate value for the velocity of light in a vacuum which was found to be slightly higher than its velocity in air. The approximate values for the velo- city of light, C, in air are C = 300,000 kilometres per second or 3 X 10^® centimetres per second or C = 186,000 miles per second. The velocity of light is a most important physical determination, since it is the speed with which many forms of
energy travel through space. It is interesting to note that the vast distances of space are measured in terms of the light-year. This is the distance travelled 180 NATURE AND PROPAGATION OF LIGHT Sec. IV: 7 by light in one year. Some of the more distant stars and nebulae are so remote from the earth that the light by which we now see them set out on its journey to the earth thousands of years ago. IV: 7 THEORIES OF LIGHT The first rational attempt to explain the propagation of light was made by Isaac Newton (1642-1728). His Sir the Emission or Corpuscular theory, Theory, postulated that light energy was conveyed through space by a swiftly moving stream of particles or corpuscles shot out from the luminous body. Most of the properties of light known at Newton’s time such as the rectilinear propagation of light and the effects of reflection (Chap. 17) and of refraction (Chap. 18) were adequately accounted for by this theory. A rival postulate was put forward by Christian Huygens (1629-1695), the son of a Dutch diplomat and poet. He sought to explain the behaviour of light in terms of waves, and hence his theory is called the Wave Theory. Again, reflection and refraction were readily explicable in terms of this wave theory. Difficulties were encountered, however, when seeking to explain the rectilinear propagation of light, and also in the need for postulating the existence of a medium, the ether, completely filling space in which the waves could travel. As *a result, the wave theory remained undeveloped and Newton’s corpuscular theory was generally accepted. nineteenth the century, Thomas Young (1773-1829), and A. J. Fresnel (1788-1827), provided valuable Early in experimental support for the wave theory of light. They were able to show that two beams of light could be made to interfere with and to reinforce each other, thereby producing alternate dark and bright lines. This could only be explained by “superposition of waves”. At one position when in opposite phase, a crest with a trough, these waves produce a dark line. At another position when in the same phase, a crest with a crest, or a trough with a trough, they produce a bright line. (Compare with superposition of sound waves. Sec. 11:6.) Another line of experimental support in favour of
the wave theory was to show that the velocity of light is smaller in the denser of two media. The corpuscular theory had predicted the exact reverse of this. Recent work seems to favour a combination of the corpuscular and wave theories in the explanation of many of the observed effects. This theory called the Quantum Theory, was first devised by Max Planck in 1901. According to this theory, light is emitted by the atoms of a luminous body in separate packets or bundles of energy called quanta or photons. Probably one or more of the electrons revolving about the nucleus of an atom ( Sec. V : 1 2 ) can be made to jump from one orbit or “energy level” to another. As they do so, one or more quanta of energy, or photons are emitradiates from the ted. luminous body as electromagnetic waves (Sec. IV: 38). The energy content of a photon determines the length and frequency of the wave, and hence the colour of the light observed. energy This 181 Chap. 16 IV : 8 LIGHT QUESTIONS. (b) How many minutes are required for light to travel from the sun to the earth (93X10^ miles)? (c) What is a light-year? 8 What contributions Newton, Huygens and Planck make to a theory of did light? 1. Calculate the distance of an object 12 ft. high whose image is 4 in. high in a pin-hole camera 10 in. long. 2. Calculate the size of the image of a tree 30 ft. high, 100 yards distant, in a pin-hole camera 8 in. long. 3. Calculate the height of a building 300 metres distant which produces an image 2.5 cm. high in a pin-hole camera 2.0 in. long. 4. How long does it take for light to 0' travel from the moon to the earth (24 X 1 miles)? 5. Calculate the number of (a) miles, (b) kilometres in 1 light-year. 6. Sirius, the brightest star in the sky, is 9 light-years away. How far away is this In miles? 7. Our nearest neighbour among the stars, excepting the sun, is Proxima Centauri which is about 25X 1 0’^ miles away. How long does it take for light from this star to reach us? 1. 2. 3. 4. 5. (a) Define optics. (b)

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