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, which con- sists of a double-walled glass vessel, the space between the walls being exhausted as completely as possible. Traces of mercury vapor are left in this space ; and at low temperatures this, freezes, forming a metallic surface over the glass walls. Fio. 112. — Dewar flask. CHAPTER XI CHANGES IN VOLUME AND PR... |
of the edges at t^ and?2, m2, n2 their lengths at £2°, the correspond- ing volumes are l^n^ and Z2w2w2; and the change in volume is?2W2W2 ~~ liminr The change in length of any straight line in the surface of a solid or of any straight edge may be measured by various means. The body is immersed in a bath of some fluid,... |
0.000019. 0.0000168. 0.0000083. 0.0000121 0.0000090 Copper Glass. Iron Platinum Steel (annealed).. 0.000011 Steel alloyed with 36% nickel... 0.00000087 Zinc, 0.0000292 Illustration of Expansion. — The fact that the coefficients of expansion of different bodies are different is often made use of to neutralize the expan... |
with a tube attached, if the liquid tills the hull. ;md pan,,f the tube, it is observed that, when the l>ull> is heated suddenly hy immersing it in a basin of hot i «>r in any other \va\, the top of the column of liquid 234 UK AT in the tube immediately sinks and then rises gradually, ascending finally higher than it ... |
it 1 + bQt replace b. The coefficient of expansion is found to be different for CHANGES IN VOLUME AND PRESSURE 235 different liquids, as is shown in the following table. It should b»- noted that the expansion of liquids is, in general, m in -h greater than that of solids. Kthyl alcohol.. between 0° and 80° C. 0.00104 ... |
in the form of a W- with a cross tube at the 236 HEAT top, as shown in the cut ; this last has a small opening -4 near its middle point and is kept horizontal ; there is a branch tube joined to the apparatus at B, which is con- nected with a reservoir K containing air that can be compressed to a pressure greater than ... |
were to hold for a gas as the pressure became smaller and smaller and finally vanished without the volume at the same time being made infinitely great, the temperature of this condition would be given by T = 0, or t° C = - - = - 273° C. approximately. Similarly, if the same law could be applied to a gas as its volume ... |
densities of gases, because P is the pressure of a gas at temperature T when the density is such that there are N1 mols in a unit volume. It is found to be 8.28 x 107 on the C. G. S. system. Energy Relations during Expansion Mechanical Expansion. — When the dimensions of a body are increased, either by the addition of... |
, or if it is a solid immersed in a fluid, the amount of external work done equals the product of the increase in volume by the pressure. (See page 159.) The internal changes consist of change in kinetic energy and change in potential energy. The first of • •is connected intimately with changes in temperature, as has b... |
vessel to expand -udd.-nly. I f t li.-n- an- nuclei in tin- air. drops of water will!»«> loosed around them, thus forming a visil.li- mist and showing that the air has been chilled. (See page 186.) This is the explanation in many cases of the formation of clouds in the air. Expansion of a Gas in General. — When a comp... |
nozzle is being used practically in recent machines for the liquefaction of gases. (See page 280.) CHAPTER XII CHANGES IN TEMPERATURE Energy Relations when the Temperature is Raised. — It is 1)\ tin- change in temperature of bodies when exposed to some "source of heat" that our attention is directed to heat phenomena ... |
difference in the amounts of heat energy added must equal the difference in the amounts of the external work done. Special Case of a Gas. — For various reasons, partly prac- tical and partly theoretical, the change in temperature of a gas is considered, as a rule, under two different conditions : (1), when the volume ... |
be shown later that 536 calories, approximately, are given out by 1 g. of steam when it condenses into water at 100° C. So, if m grams are condensed by the body at this temperature, it must receive 536 m calories. "Specific Heat." — The number of calories that must be added to a body whose mass is 1 g. in order to rai... |
referred to above there are, then, three methods for the measurement of specific heat of a given substance. We assume in each case that there is no loss of heat by radiation, etc. 1. Method of Mixtures. If iw, = mass of body, wij = mass of water, /, = original temperature of the body, fa = original temperature of the ... |
~ ll) ~ 536 m2' With this method there is a correction for the water equivalent of the calorimeter; and one of the chief difficulties is to measure accurately the quantity of steam condensed. The apparatus used was invented by Professor Joly of Dublin. Specific Heats of a Gas. — Any one of these methods can be used to... |
in a unit volume of the gas, the energy of the molecules in this volume is then \mW^N. But wiN is the mass of the molecules in this volume; so the internal energy of a unit mass of the gas is \ bVz. This can be expressed in terms of the temperature; for the pressure of a gas is given by the formula p = dRT, if d is th... |
031 Mercury. Paraffin. Platinum Bihra Tin r, Water. Turpenti iii-. 20°-50°C.. 0°-100°C.. 0°-100°C.. 0°-100°C.. 0.o:W 0.0:^:5 0.467 1.00 Air.... j Chlorine. Carbon dioxide (JASKS. o.i»:J7.. 0.1'Jl.. O.'JO'J Of 0.171 "iv.; RATIO. l.40i. 1.06. ; l.:to 256 HEAT GASES — Continued Cp Cv RATIO Helium Hydrogen.... 3.40.. 2.40 ... |
showing they have received energy ; when an acid or salt is dissolved in water, its temperature is changed; when water freezes or dew is formed, the temperature of the surrounding air is raised slightly, etc. During these changes of state, not alone are there heat changes, but alteration in volume, and so external wor... |
decrease in pressure will cause some of the water to freeze, showing that the melting point has been raised and heat energy flows out from the water into the surround- ing region. The explanation of this variation of the melting point with the external pressure depends upon the fact that when a solid melts its volume ... |
in contact with ice at a temperature below 0°, and it will there- fore immediately freeze again. This is the explanation of t he formation of snowballs ; and this action also plays a most important part in the motion of glaciers. The phenomenon is called "regelation." n<>ti<m <>f :i in : is due to the fact that the ic... |
of a unit mass of water one degree Centigrade, and define heat of fusion as that number of these heat units which is required to melt a unit mass of the substance, quite regardless of the size of the unit mass.) This energy is spent in overcoming molecular forces and in doing external work if the body expands on r//.i... |
pure solvent, in general ; so that the solution becomes more concentrated. (In certain cases some of the dissolved substance is caught in the meshes of the solid solvent ; but this is a mechanical process, not a thermal one.) Then, in order to freeze out more of the pure solvent, the temperature must be lowered still ... |
C. 415° C. 80 23-33 5.86 2.82 9.37 28.1 Evaporation Boiling Point. — If a liquid stands in an open vessel ex- 1 to the air, it is observed that the quantity of liquid continually diminishes ; it is said to " evaporate " ; the sub- stance passes from the liquid to the gaseous condition. The gas rising from a liquid is c... |
; while, if the temperature is lowered, the pressure decreases, and some of the vapor condenses to form more liquid. If the tem- perature is kept constant, however, the pressure remains the same, entirely independent of whether there is a small or a large amount of liquid present. This condition may be called one of s... |
* illtintrmtlnjr tl preMare of Mtnrated vapor : » umall u ll.ini.l. t.g. water, to Introduced there tl the liquid will evaporate, and equilibrium will lx» reached at a pressure d. -pending upon the temperature. This ma\ 266 HEAT be varied at will by surrounding the tube with a bath of some liquid whose temperatures can... |
temperature of boiling water is much less than 100° C. on a mountain top ; by the high tem- perature in steam boilers where the pressure is great, etc. From the description given above of the statical method, it is seen that there are two general methods available for con- dt nsiii'^ a vapor into a liquid : one is to ... |
- tity of water vapor in a unit volume corresponding to various dew-points is given in tables ; e.g. if the dew-point is 10° C., the mass per cubic metre is 9.3 g. The pressure of this vapor corresponding to 10° C. is 0.914 cm. of mercury ; thus, if the barometric pressure is 76 cm., the pres- sure due to the air is 75... |
attached to an air CIIAM.I: <>r >TATE 271 care being exercised to guard against any possible conduc- tion of heat to the water; as the air is exhausted, thus diminishing the pressure on the water and removing the vapor, the water evaporates so rapidly that the heat energy required is taken from the water left behind, ... |
of the steam in the boiler as Imi^ as the connection is maintained; but after the supply of steam is cut off, the steam, as it expands, decreases in pres- sure. In the meantime the pressure in the cylinder on the other side of the piston has been made as small as possible 272 HEAT by one of three methods: (1) by openi... |
heat energy is given out by the steam. The steam does work in pushing on the piston, and work is done on it and on the water formed from it when the piston performs its reverse motion. If H is the heat energy received at the temperature of the boiler, and W is the net external work W H. done, the ratio -= is called th... |
, as the isothermals at higher and higher temperature are drawn, they have the same general shape, but the horizontal portions become shorter, until a temperature is reached, the isothermal for which has no horizontal portion. This is called the "critical" temperature. For temperatures higher than it, the isothermals a... |
is reached that corresponds to the state of saturation of the vapor for the temperature. After this, any further decrease in volume or temperature will cause the vapor to condense. The values of the critical temperatures for various gases are given in the accompanying table : CRITICAL TEMPERATUI:I - Alcohol... 243°.6C... |
., etl, - a thlrtl ring the g«* thr»ui;li //.''. • Nrft|K- tliniinrh hjr the rod f. As the gas escni <lrawn out through t a-« It rises it c<>. 282 HEAT The melting point of hydrogen is estimated at — 257° C. ; and the max- imum density of liquid hydrogen is 0.086. By allowing a quantity of liquid air to evaporate slowl... |
a suitable pressure ami temperature are applied. (This i> one step in Moissan's method of making artificial diamonds. ) The number of calories required to make one gram of a solid sublime at a definite temperature is called the "Heat of Sublimation." It equals the sum of the Heats of Fusion and of Evaporation at that ... |
now heat energy is added, the sol- vent will dissolve more of the substance ; and if heat energy is withdrawn, the solvent will precipitate some of its dissolved substance ; because in this last case, for instance, if the effect were to make the solution more soluble, this act of solution would withdraw some heat ener... |
monoxide (CO), -11<» calories are evolved: and if this is converted into carbon dioxide (CO2), 5720 more calories are involved — 7860 in all. And, if the same amount of carbon is oxidized at once into carbon dioxide, the heat involved is the same. This is an illustration of the Conservation of Energy. A few illustrati... |
when the heat energy is applied to its lower portions. It should be noted that the energy is gained by the portions at low temperature and is lost by those at a higher temperature. This method of distribution of heat energy is the one that forms the basis of the ordinary means of heating houses, — hot-air furnaces and... |
ial that lost at the surface of the rod by convention 1 radiation), -iuce the rod i- in a steady state. It is important to note that the heat energy is conducted from the hotter portions of matter to the colder ones. When the >t in a steady state, e.g. immediately after one end is 288 BEAT put in the fire, part of the ... |
space CONVECTION, CONDUCTION. AND HA />/ J77OJV 289 between completely exhausted of air. I>\ using a Dewar tlask (sec page -'28), liquid air and hydrogen may be kept for hours in a room at ordinary temperatures. Illustrations. — The fact that metals conduct well is shown by count- less experiments. Thus, if a piece of... |
\ it \ in terms of the mean free path, etc. (See page 202.) The conduetU ;i few bodies at 0° C. are given in the following tahle, in which the heat unit is a calorie and the C.G.S. system is \\«-<\: AMES'S PHYSICS — 10 HEAT Silver 1.096 Copper 0.82 Aluminium 0.34 Zinc 0.307 Iron 0.16 Mercury 0.0148 Water 0.0012 Radiati... |
for it is evi- dent that a medium through which waves are passing has both kinetic and potential energy. Thus, as waves advance into a medium, energy is carried forward, owing to the action of the particles of the medium on each other. We say, then, that "waves carry energy," although of course this energy is associat... |
num- ber of vibrations per second is 3 x 1010 x 104 or 3 x 1014, i.e. 300 trillions. Consequently these vibrating particles are thought to be the infinitesimal parts of a molecule. Our conception, then, of the structure of ordinary matter is as follows : it consists of molecules which are moving to and fro, vibrating ... |
glass is not, — and containing a fine vertical quartz fibre which carries a horizontal arm; to each end of this is attached a thin piece of mica, polished on one side and blackened on the other. The blackened face of one mica disk comes opposite and parallel to the fluorite window; so, if radiation enters this, it fal... |
ipMnent \\a\cs, vertieal distances to represent quantities "f energy carried by the individual trains of waves. Several eurves are given of the radiation from blackened copper at different temperatures. It is seen that these curves are in •!-d with tin- statements made above. If we consider any individual wave length a... |
a constant. These two laws, which have been verified over wide ranges of temperature by most painstaking investigations, offer con- venient means of obtaining the temperature of bodies when they are so hot as to render it inconvenient to use ordinary CO.\T7-:<T/M.\. CQNDUi rfOJT, -i.v/; HAhiATioy 297 means. If we assu... |
mit ted. A body which allows waves of a certain wave length 298 HEAT to pass through it is said to be "transparent" to them/ but no body is perfectly transparent to any waves ; if it is suffi- ciently thick, it will absorb them. In a thin layer, however, a body may absorb certain waves completely and may trans- mit ot... |
t IK-SI- vibrating particles emit waves immediately, without the temperature sensibly rising. This is the case with pieces of fluor spar, thin layers of kerosene oil, and with a few other bodies, as will be shown later under Fluores- cence and Phosphorescence. In other bodies the absorbed • •ii'Tgy is distributed amon... |
excludes fluorescence, phosphorescence, etc. If several bodies at different temperatures could be inclosed inside a vessel which absolutely prevents any heat energy from entering or leaving, and which keeps a constant volume (so that no external work is done), there is every reason for believing that equilibrium would... |
stirred in it. it appears colored when viewed from any direction.) Then, if such a red body is heated until its temperature is suiliciently high, it will emit all the waves except those which < -spend to the sensation of red, and so, if viewed in a dark room, will appear bluish green. This law connecting radiation and... |
itself is absorbed by them, and they radiate a certain proportion back toward the earth. Our appreciation of the temperature of the air in which we live depends largely upon the quantity of heat energy absorbed by the air, not so much upon the radiation received by us directly from the sun. Thus we see the reason why ... |
the specific heat of water was the same at all temperatures ; and in the early work no distinction was made between the amounts of energy required to raise the temperature of water between different degrees. Robert Mayer calculated the mechanical equivalent from experimental data secured by other observers on the heat... |
energy received, and Hv that lost, and W the ex- ternal work done, W= Hl — N2 by the conservation of energy (using the same units for heat energy and external H\ work), and the efficiency is * — 2. In discussing the TT __ TT action of this engine Carnot was led to several most impor- tant conclusions which Clausius an... |
to each temperature reading the reciprocal of the coefficient of expansion of the gas, i.e. 273 approximately. (This is what we have called on page 240 "absolute gas temperature.") Thus, if large quantities of boiling water and in» -It ing ice could be used as the reservoirs between which a Carnot engine worked, the q... |
uring the process of combustion a material substance, called "phlogiston," was given off; and this idea persisted until the \\ork of Lavoisier, about 1800, and even later. Fan- tastic theories in regard to the properties of phlogiston and of the substance heat (or "caloric") were of necessity brought forward in order t... |
a ther- mometer. Herschel speaks of these rays as subject to the laws of reflection and refraction; and this fact was fully established by Melloni some thirty years later. It was proved in the following years that these rays could be dif- fracted, be made to interfere, be polarized, etc.; and that, in short, they were... |
ragm of a telephone instrument ; if one end of a long, stretched rope is fastened to a movable object and if the other is given a sudden side wise or lentil i\\ ise motion, a disturbance will pass along the rope and will do work on the object; etc. In all these cases it is evident that there is a vibrating centre which... |
and down of a stick dipping in the water, waves spread out, owing to the fact that the force of gravity tends to maintain a level surface. Again, if a vertical cord, like a fishing line, is moved sidewise through the surface of a pond (or, if a quietly flowing river flows past a stationary vertical cord), short waves ... |
verse t rain of waves is produced in a long, stretched rope by n loving one end up and down in a vertical line, the rope will at any instant have a sinuous form when viewed from ide, but will appear straight when viewed from above. In this case all the particles are vibrating in straight lines through which a plane ca... |
t and A are taken smaller and smaller.) Detection of Waves. — The effect of the waves is perceived in two ways. If the medium is limited in one direction by \\ ATE MOTION 315 e object, with which it is connected in such a mannei that the vibration of this object would produce waves in the medium, this will be set in m... |
t increases gradually but OOD- tn.'i..-. :\- with the depth; the rate of increase varies greatly with the VIBRATION H AND WAVES geological conditions, but is on the average about 1° C. for a depth of 28 m. This condition requires that heat energy should be continually flowing from the interior of the earth to the surfa... |
AND COMPLEX VIBRATIONS \Vi: shall now proceed to discuss in detail the two funda- mental features of waves : liist. the properties of the centre of disturbance; second, those of the medium through which the waves pass. The effects produced when waves in the air or in the ether are perceived by our senses of hearing or... |
nt — ctj) -f A2 cos (nt — a2). By ordinary trigonometrical formulae this takes the form x = A cos (nt — a), where A2 = Af + A22 + 2 AlAl cos (a, - a2), A, sin a, + A „ sin a9 and tan a = -^ — • A l cos ax + A 2 cos a2 This shows that the resulting motion has the same period as that of its two components, but a differen... |
phase, l><»th will he repre- sented by the point 0 at the same instant; then, when one vil. ration has reached /',. the nth.-r.ha8 reached Ql ; and the geometrical sum is given by Rr When the fnrmer \ il»i at inn reaches PT the latter rca< -In •- '/, : and the geometrical sum is givm l>\ /{., : etc. It is fvid.-nt tha... |
of glass ; but in this case the kept stationary and the pendulum is set swinging, not in a plane through its origin, but in a cone, as a result of a sidewise push given it when it is held out at the end of its swing. Another method, due to Lissajous, is to use two large tuning forks whose frequencies are the same, and... |
rapid, as for in- stance if a pendu- F.G. 145. - A damped vibration. lum has a plCCC of paper fastened to it, the period is sensibly increased. This decrease in ampli- tude is due to loss of energy by the vibrating body, generally by friction as it moves through the air or at the pivot. This is evident if we calculate... |
a child in a swing being set in motion by a series of pushes given at intervals agreeing exactly with the natural period of the swing has been mentioned already. In a similar manner a heavy church bell may be set swinging. If a tun- ing fork is vibrating near another one of the same frequency, tin- latter will be set ... |
different distances from the source. Let us describe two spherical surfaces of radii rl and r2 around the source ; their areas are 4<7rr12 and 4?rr22. So if the source emits in a unit of time an amount of energy equal to E, and if there is no absorption by the medium, the intensity at any point of the first surface Tf... |
res- sion in the springs of the slow set. An expansion, then, propagated along the slow set produces an expansion in the fast one, but a compression is reflected back along the slow one. If a series of waves consisting of alternate compressions and expansions, such as would be produced in this model by giving harmonic ... |
st ant velocity v. Let us consider the motion of the particles of the cord as the curved portion of the tube reaches it, and the forces which the tube exerts on the cord. As this curved P Q F i... 149. — A cord, over which has been slipped a bent tube, is stretched between Pand Q. portion of the tube reaches any parti... |
defined under which the change in volume occurs (see page 194). In the present case, the number of compressions and expansions in one second is so great that the change in volume of the fluid takes place adiabatically ; for there is not time for heat transfer to occur. Consequently in the above formula E is the adiaba... |
at 8° C. it is found, as stated before (page 172), that an increase in pressure of one atmosphere, i.e. of 76 cm. of mercury, decreases a unit volume by 0.000047 of its value. If the thermal effects may be neglected, „ 76 x 981 x 13.59, 7, therefore, V= 145,000 cm. per second. -£666617 — 'and'/ = There are also experi... |
. ) Water Waves. — Tin- velocity of waves upon the surface of a liquid di-j.rmls upon many quantities, and we can do no 340 r//;/,M770ATs AMD WAVES more here than state certain facts in regard to liquids whose viscosity may be neglected. These statements involve the quantity known as the " wave length," which in the ca... |
electric waves along wires. But it may be stated that in both these cases part of the energy of the waves is dissipated in heat effects throughout the media and in other ways, and as a consequence of this the waves die down and are not propagated as far as they otherwise would be. The FIG. 151. — A drawing1 of Lyman's... |
wave length, and so in a unit of time the waves advance a distance equal to the product of the wave number and the wave length. Therefore, if V is the velocity of the waves, I the wave length, and ^V the wave number, V— Nl. Or, if T is the period of the waves, V= —. (The velocity of an individual particle depends upon... |
- vibrating source is approaching it in a straight line with the velocity v, the case is entirely different. If tin- source were n«>i the length «,f ;v wave would be I; but. when it is the wave fnmt advances a distance T from the in,i unit time, and in this same time the source advances a diMam-e v; so the X \\aves tha... |
medium are inci- dent upon a boundary separating it from another in which the velocity is different (see page 333), waves are transmitted into the latter medium, and waves are also reflected back into the former. The combined intensity of these two trains of waves must equal that of the incident train ; and so the amp... |
periodic or a confused vibration ; it will produce a corresponding wave. If the disturbance is intense, but lasts only a short time, it produces in the medium what we have called a "pulse." Its effect when it reaches a portion of the medium containing foreign matter is naturally different from that of a long train of h... |
the motion of the hand is exactly right, it will be observed that the cord ceases to have the appear- ance of being traversed by waves, and vibrates transversely in one or two or more portions or " segments." That is, there are certain joints in the cord where there is very little, almost no, motion, which are called ... |
hand is approximately one, as is evident if one observes the motion. If the long flexible cord is held suspended vertically from a balcony so that the lower end hangs free, a vibration of the same kind can be produced ; only in this case, since reflection takes place at a " free end," this point is a loop. As the freq... |
formula, * d IT r=\' —, where T is the tension in the cord and d is the mass per unit length. Substituting this in the general for- mula, we have N= ^'^\—', which shows that if the tension of cord is increased, the frequency is increased ; if the length of the cord is increased, the frequency is decreased; etc. All of... |
. 157. — Stationary vibration in a column of gas. Vertical lines represent positions of layers of gas. Curves represent by their vertical displacements the horizontal displacements of the layers of gas from their positions of equilibrium. Arrows represent the directions of motion of the layers of gas. ing the gas is a ... |
356 \'li;ilATlONS AND WAVES distance from loop to loop is the length of the column, neglect- 2 2JV, ing the slight correction for the ends ; and so L = -1 = -—, The next simplest case is when there is a loop at the middle point and a node at each of the points halfway from it to the ends. The distance from loop to loo... |
is bowed or struck so as to be set in vibration. The frequency of a fork may be measured with great accuracy by comparing its period with that of a standard clock ; but for details of the methods of comparison, reference should be made to some larger text-book, such as Poynting and Thomson, Sound, Chapter III, or to s... |
transverse or longitudinal vibrations. The simplest mode of transverse vibration is shown in the cut. The position of the loops is fixed by the I MI i 1 1 1 where the clapper strikes. Many other vibrations than the fundamental are always present, but there is no simple relation between their frequen- It there ll an ir... |
waves in different media. Thus, suppose two stretched cords have the same frequency of vibration when vibrating transversely in their fundamental modes ; then if L^ and L^ are their lengths, and Vl and F^ are the velocities of transverse waves along them, •• BTA /vo.v.i/;)' HMFJ&S" 363 Similarly, if the fundamental lo... |
to a large box open at its ends ; place loosely on the cord or wire a light saddle of paper ; set the stem of the vibrating tuning fork 364 VIBRATIONS AND WAVES on the box ; if there is resonance, the wire or cord will be set in vibration and the paper saddle will be thrown off. Kundt's Method. — We can also compare t... |
the solid rod is extremely small compared with that at a loop in the gas. The explanation of the formation of the transverse ridges of the pow- der depends upon the fact that, as the particles of gas away from the nodes vibrate back and forward between the particles of powder, their mean velocity depends upon the arra... |
motion is in part due to Huygens, and it is called by his name. In its most general form it is com- plicated, and can be demonstrated only by the aid of the infinitesimal calculus. We shall give certain special applica- tions of it ; and, although the statements to follow are not rigorous, they are sufficiently so for... |
We shall also quote Huygens in his explanation of reflec- tion and n-fractioii. 1. Reflection of Plane Waves by a Plane Mirror. — " Having explained the effects produced by light waves in a homogene- ous medium, we shall next consider what happens when they impinge upon other bodies. First of all we shall see how refl... |
straight line BGr, which is drawn parallel to AC. But, as is easily seen, all these circles have a common tangent in the straight line BN, viz., the same line which passes through B and is tangent to the first circle having A as centre and AN, equal to BC, as radius. " This line BN (lying between B and the point N, th... |
right angles, i.e. the plane of incidence]. "It is thus seen that the spherical second a r\ waves can have no common tangent plane other than BN. In this plane will he located more of the reflected motion than in any other, and it will therefore receive the light transmitted from the \\.ive CH. ******* VM! -'« I II •,... |
ii would equal the whole lengths of the various lines KM. " But all these circles have a common tangent in the line BN\ viz., the same line which we drew from the point B tangent to the circle SNR first considered. For it is easy to see that all the other circles from B up to the point of contact N touch, in the same m... |
ratio of BCto AN is the same as that of the speeds of light in the media on the side toward AE and the side inward AF, respectively; hence, also, the sine of the angle DAE bears to the sine of the angle NAF the same ratio as these two speeds of light." Since these speeds are properties of the media and not of the dire... |
of waves sent out by having some source placed near a long Marrow slit in an opaque screen. If the slit is sufficiently narrow, the disturbances will proceed out from the slit in all directions, making a train of waves with a cylindrical wave front. A second opaque screen with two X' if row slits, which are close toge... |
are seen. Similarly, if short sound waves are used, it is not difficult to prove by means of a sensitive flame (see page 192) that there are corresponding " bands of silence and sound," meaning that at points along a line parallel to the slits there are disturbances in the air, while along a neighboring line there are... |
the screens, and that of the sources are known, the wave length may be determined. This matter will be referred to later. It should be noted that in the formation of these interfer- ence fringes there is no destruction of energy ; it is simply distributed differently from what it would be if the screen t: A.\h Dll-'Fl... |
two light waves annulling one another when they are half a wave length apart. The formulae of interference just given do not apply to the case of a single wave, not to mention the fact that such waves do not occur in nature. /A'/-/-;/,- /••/•;/,• /-;.v< B.i.v/> inrni ACTION 381 are equal to the resultant of all the di... |
ically VIBRATIONS AND WAVES It is evident that the effect at P of the secondary waves from any point Q on the wave front depends upon the length of the line QP for two rea- sons : the decrease in amplitude of spherical waves varies inversely as the distance, and the phase of the disturbance as it reaches P varies with ... |
at d n. iliime. Tim area of this 386 VIBRATIONS AND II zone is wla very approximately, if - is ;i small quantity. a (For visible ether waves I is not far from 0.00005 cm., and so if a = 10 cm., the area Trla equals 0.0016 sq. cm.) Spherical Waves. — The case.of spherical or cylindrical waves may be treated in the same ... |
sufficiently large, e.g. a mountain. But we see that, if the waves are long and the obstacle is of ordinary size, the former will penetrate a great distance in the shadow. This phenomenon of the peculiarities of a shadow produced by trains of waves incident upon an obstacle is called " dif- fraction." It was first des... |
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