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we can use a device designed to intentionally break that continuity (called a switch). This switch can be mounted at any convenient location that we can run wires to. It controls the ow of electrons in the hole circuit: 253 switch Battery - + It doesn’t matter how twisted or convoluted a route the wires take conductin...
oking "horseshoe" symbol is the capital Greek letter › (called omega), just a character in a foreign alphabet (apologies to any Greek readers here). Aside: Each unit of measurement is named after a famous experimenter in electricity: The amp after the Frenchman Andre M. Ampere, the volt after the Italian Alessandro Vol...
ge may be. Since P = IV and I = 0, the power dissipated in any open circuit must be zero. 14.11 Calculating electric power We’ve seen the formula for determining the power in an electric circuit: by multiplying the voltage in volts by the current in Amperes we arrive at an answer in watts." Let’s apply this to a circui...
3 common to 1, that same 10 volts also exists between these other pairs of points: Between points 1 and 4 = 10 volts Between points 2 and 4 = 10 volts Between points 3 and 4 = 10 volts (directly across the resistor) Between points 1 and 5 = 10 volts Between points 2 and 5 = 10 volts Between points 3 and 5 = 10 volts B...
it will ow in a counter-clockwise direction, from point 4 to 3 to 2 to 1 and back to 4. However, we have one source of voltage and three resistances. How do we use Ohm’s Law here? An important caveat to Ohm’s Law is that all quantities (voltage, current, resistance, and power) must relate to each other in terms of the ...
I2 + I3 Finally, applying Ohm’s Law to the rightmost ("Total") column, we can calculate the total circuit resistance: R1 9 0.9m 10k E I R R2 9 4.5m 2k R3 9 9m 1k Total 9 Volts 14.4m Amps 625 Ohms Rtotal = Etotal Itotal = 9 V 14.4 mA = 625 W Ohm’s Law Please note something very important here. The total circuit resista...
Resistance is the measure of opposition to electric current. A short circuit is an electric circuit oﬁering little or no resistance to the ow of electrons. Short circuits are dangerous with high voltage power sources because the high currents encountered can cause large amounts of heat energy to be released. An open ci...
istinguishes the Earth magnetically from a bar magnet is its magnetosphere. A magnetosphere is the region around an astronomical object, in which phenomena are dominated by its magnetic ﬂeld. Earth is surrounded by a magnetosphere, as are the magnetized planets Jupiter, Saturn, Uranus and Neptune. Mercury is magnetized...
change of the magnetic ﬂeld ux with induced voltage (note the use of a lower-case letter "e" for voltage. This refers to instantaneous voltage, or voltage at a speciﬂc point in time, rather than a steady, stable voltage.): e = N dF dt Where, e = (Instantaneous) induced voltage in volts N = F = t = Number of turns in wi...
(few teeth) high torque low speed + + low torque high speed "Step-down" transformer high voltage AC voltage source many turns low voltage few turns Load high current low current If the winding ratio is reversed so that the primary coil has less turns than the secondary coil, the transformer "steps up" the voltage from...
he rate of alternation by measuring the time it takes for a wave to evolve before it repeats itself (the "period"), and express this as cycles per unit time, or "frequency." In music, frequency is the same as pitch, which is the essential property distinguishing one note from another. However, we encounter a measuremen...
rent through the coil will be in-phase with the ux wave: e = voltage F = magnetic flux i = coil current e F i This is why alternating current through an inductor lags the applied voltage waveform by 90o: because that is what is required to produce a changing magnetic ux whose rate-of-change produces an opposing voltage...
c symbols of all light-emitting semiconductor devices. Conversely, if a device is lightactivated (meaning that incoming light stimulates it), then the symbol will have two small arrows pointing toward it. It is interesting to note, though, that LEDs are capable of acting as lightsensing devices: they will generate a sm...
or a polymer. Polymer materials can be exible; such LEDs are known as PLEDs or FLEDs. Compared with regular LEDs, OLEDs are lighter and polymer LEDs can have the added beneﬂt of being exible. Some possible future applications of OLEDs could be: Light sources Wall decorations Luminous cloth † † † LED applications Here i...
NP is really arbitrary. All that matters is that the proper current directions are maintained for the sake of correct junction biasing (electron ow going against the transistor symbol’s arrow). Going back to the NPN transistor in our example circuit, we are faced with the need to add something more so that we can have ...
uction channel. These have become quite popular. 16.4 principles of digital electronics logical gates, counting circuits 16.4.1 Electronic logic gates The simplest form of electronic logic is diode logic (DL). This allows AND and OR gates to be built, but not inverters, and so is an incomplete form of logic. To built a...
ng Fact: The word atom is derived from the Greek atomos, indivisible, from a-, not, and tomos, a cut. An atom is the smallest portion into which a chemical element can be divided while still retaining its properties. Atoms are the basic constituents of molecules and ordinary matter. Atoms are composed of subatomic part...
icted sense, to include theories like quantum ﬂeld theory. Quantum mechanics is the underlying theory of many ﬂelds of physics and chemistry, includ- ing condensed matter physics, quantum chemistry, and particle physics. 17.9 Pauli exclusion principle The Pauli exclusion principle is a quantum mechanical principle whic...
light did not seem to act as a wave) by postulating the existence of photons, quanta of energy with particulate qualities. Einstein postulated that light’s frequency, ?, is related to the energy, E, of its photons: E = hf 10¡34Js). (18.1) where h is Planck’s constant (6:626 £ In 1924, De Broglie claimed that all matter...
is denoted by letter A. Standard nuclear notation shows the chemical symbol, the mass number and the atomic number of the isotope. number of nucleons number of protons A ZX chemical symbol For example, the iron nucleus (26-th place in the Mendeleev’s periodic table of the elements) with 26 protons and 30 neutrons is d...
mark. 351 Before striking the screen, this ux passes through magnetic ﬂeld, which is perpendicular to velocity of the nuclei. As a result, the ux is deected to certain angle. The greater the mass, the smaller is the angle (because of inertia). Thus, measuring the displacement of the mark from the center of the screen,...
er another 24 hours only 125000 will remain and so on. The number of unstable nuclei that are still \alive" continuously decreases with time according to the curve shown in Fig. 19.2. If initially, at time t = 0, their number is N0, then after certain time interval T1=2 only half of these nuclei will remain, namely, 1 ...
ppealing visualization of subnuclear collisions. 19.7.6 Spark chamber Spark chamber is a historic device using electric discharges over a gap between two electrodes with large potential diﬁerence, to render passing particles visible. Sparks occurred where the gas had been ionized. Most often, multiple short gaps were u...
il, and the reactor will not crack, melt, explode or spew hazardous wastes. It simply goes up to a designed "idle" temperature, and stays there. In that state, the reactor vessel radiates heat, but the vessel and fuel spheres remain intact and undamaged. The machinery can be repaired or the fuel can be removed. A large...
» The quantum mechanical wave function (that describes the probability density) oscillates with a frequency which is proportional to the energy of the system. With a typical binding 1017 s¡1. This means that the particle energy of a muonic molecule of 300 eV this frequency is hits the barrier with this frequency and du...
f a century, experimentalists discovered so many new particles (few of them are listed in Table 19.3) that it became obvious that they cannot all be elementary. When colliding with each other, they produce some other particles. Mutual transformations of the particles is their main property. family photon leptons hadron...
such diagrams that will describe possible particle transformations. The only rule is to keep the lines continuous. They can disappear or emerge only for a quark-antiquark pair of the same avor. However, the continuity of the quark lines is valid only for the processes caused by the strong interaction. Indeed, the ﬂ-de...
th calculations) how that development proceeded step by step. During the expansion, all the nuclei and atoms in the cosmos were created. The amounts of diﬁerent nuclei are not the same. Why? Their relative abundances were determined by the processes in the ﬂrst moments after the explosion. Thus, comparing what follows ...
wardly with generic text editors or (for images composed of pixels) generic paint programs or (for drawings) some widely available drawing editor, and that is suitable for input to text formatters or for automatic translation to a variety of formats suitable for input to text formatters. A copy made in an otherwise Tra...
nder this License, under the terms deﬂned in section A above for modiﬂed versions, provided that you include in the combination all of the Invariant Sections of all of the original documents, unmodiﬂed, and list them all as Invariant Sections of your combined work in its license notice, and that you preserve all their ...
meet ; with this point of intersection as a centre and with any line as a radius, describe a circle ; let L be the length of the arc of this circle intercepted between the two lines and let R be the length of the radius of the circle ; then by definition the ratio — is the numerical value of the angle. Thus, in the fi...
ng the mean value of a series of quantities. equal. The importance in the average of a given value, e.g. am, is the length of time it lasts. The actual quantity dur- ing the interval T2 — T^ is changing from a1 to «2 ; during the interval T8— T2 it is changing from a2 to #3 ; etc. As an approximation, let us assume tha...
hat the velocity at any point is char- acterized by the value of the speed and by the direction and "sense" of the tangent to the path at that point. If the motion is uniform along a straight line, that is, if the velocity is constant (both in amount and in direction), the speed is equal numerically to the distance tra...
act, it is a quantity of no importance physically, as we shall see later. Special Cases. — There are several special cases of trans- lation which deserve detailed description owing to their groat importance in problems of Physics. KINEMATICS 43 1 . A point moves in a straight Hm- with a constant accelera- Since the acc...
therefore rh2 cos (POQ). If the displacement of Q with reference to 0 is called rr, and if it is defined to be positive when drawn to the right, cos (P0$) =-; and hence the numerical value of the K1XKMATICS 49 acceleration of Q is /r./\ its direction hein^ toward 0. which i lied the, "origin." If we cull all vectors po...
t is proportional to an infinitely small angle, and therefore two rotors representing angular velocities may be added geometrically, if the two axes lie in the same plane. Illustrations of angular velocities are common ; a few may be described as follows : that of a flywheel is given by a line having a definite sense a...
Ord with them. 60 MECHANICS 2. Principle of Independence of Action of Forces. — Again, we shall assume that, when a body is tunh'r the influence of several forces, the action of each one is independent of the actions of the others. 3. Principle of Action and Reaction. Definition of " Mass." — Then, if we have an isolat...
d observed that • lied the ground at the same instant, thus proving that they had the same acceleration. (Galileo, however, had no conception of the property of mass, and performed hi* ex- periment with a different object.) Newton was Un- to real i/e the fact that a material body had a pi < iiieh we have called -mass";...
ns of this type of force are afforded by fall- ing bodies, F= mg ; by an elevator when rising or falling at a varying rate ; a railway train "getting g and mtff are Up " speed, etc. When an elevator is rising at a uni- Tis the tension in the . FIG. 30. — Atwood'f the forces due to gravity, string. DYNAMICS 71 form rate...
trated by the motion of a boat that is being rowed across a river, there being two forces, one due to the oars, the other to the current ; and by many other similar motions. If a cord carrying at its two ends particles whose masses are ml and m2 is supported by two pulleys, and if a third particle of mass m3 is attache...
Then m^a^m^a^ — equals X. We have just shown, however, that this sum equals Jfefa, where a is the component of the acceleration of the centre of mass in the chosen direction. That is, M a = X or a = — . In words, the acceleration in any direc- tion of the centre of mass of a set of particles equals the sum of the comp...
the angular acceler- ation produced owing to it. The simplest case of a rotat- ing body that we can imagine is that of a particle attached to a pivot by a massless rod. Let the particle of mass m be at A ; let the pivot be at P ; and let there be a force F in the direction AB. Draw the perpendicular PQ upon the line o...
apply to one particle of the body ; etc. The statement that this sum is constant when the external moment is zero is still true, however. Several illustrations are worth noting, if the angular velocity of all the particles is the same, the angular moment um may be expressed (wjfj2 -f nyf + —)h\ and now, if o\viii«jf to...
round the axis through 0 equals the si 1111 of the moments of Fl and Fv Let its position be indi cated as shown in the cut, its intersection with the line OAC being at B. The condition that B must satisfy is that (F, + F2) OK = F}OA + FtOC, or FlAB = F3BC,i.e.j£ = %. This may also be expressed as follows: i.e. or These...
any way, the tendency will be for it to return to the tern- DYNAMICS 105 perature of the surrounding medium. Now, when the tem- perature of an iron bar is increased, its length is increased ; but this act of increasing in length produces a tendency for tin- bar to return to its former temperature. That is, if an iron ...
em has potential energy, it is in a condition such that it can do work. A falling body can compress a spring or bend a board, thus overcoming a force ; or it may strike another body and change its speed, thus doing work also. Similarly, a bent bow may change the speed of an arrow or it may raise a body up from the eart...
nally boil ; if an inelastic body, like a piece of lead or putty, is deformed, different layers move over one another, there is friction, and the temperature rises. These various changes — melting, boiling, rise in temperature, and expan- sion— are called "heat effects," and will be discussed more fully in the next sec...
produce friction. ( '..nsc.jucnt ly, a 'nine never delivers as much energy as it receives; i ic hitter is spent in tion u»d is therefore : " in heat effects. A -a in. if the foffM produces ieceleration of the working parts of the machine, part of the work done is thus spent in producing kinetic energy not in overcomii...
responding de- crease in the displacement ; that the direction of a force may be changed ; and that a moment may produce a force. Chemical Balance. — This is not a machine in the ordinary use of this word, but is an instrument involving the principle of the lever, which is used to determine when the weights of two bodi...
g New- s law to be true, one can at once calculate the value of a in the formula. It is 0.000000066570, or 6.6576 x 10-», 134 MECHANICS on the C. G. S. system. This leads to a value for the mass and the average density of the earth. (By the value of the " density " of a homogeneous body is meant the ratio of the value ...
can form drops or not; the former are called "liquids"; the latter, "gases." See Introduction, page 16. Elasticity. Viscosity, etc. — Some bodies when deformed slightly by a force will return to their previous condition after the force is removed; they are called "elastic." Thus, glass, steel, ivory, etc., and all flui...
g a wire. This means that the changes in the molecular forces which are called into action at any point by the defor- mation are sufficient to neutralize the action of the external force. There is thus at any point of a deformed elastic solid a change in the position of the molecules immediately around it and a corresp...
ume of the solid, the latter is as a rule made in the shape of a rod ; two fine parallel lines are scratched on it, one near each end ; and by means of a comparator the distance apart of these lines is measured before and under the compression. If 1Q is the original length and I the length when the stress is increased ...
. Energy Relation. — The potential energy of a solid in a state of strain may be deduced at once if its elastic coeffi- cients are known. (See page 110.) As an illustration con- sider a stretched wire. Using the same symbols as before, which means that the force required to produce an elonga- tion AZ is — - — ; consequ...
ny point in a fluid due to the forces between the molecules. This we cannot measure ; but we can form an estimate of its value for a liquid by measuring the amount of work required to evaporate it, assuming that we can neglect this pressure for a gas.) Pascal's Law. — Let us, then, consider the properties at the centre...
led, to ditlVrent heights and noting the change in the height of the column. Many experiments to show the effects of the atmos- phri -ir pressure were devised after the air pump was invented by Von Guericke (about 1657) and improved by Boyle. Liquid- are in general contained in open vessels which they only partially fi...
horizontal level of the rest of the surface returns, and owing to its inertia continues to rise until it is above the level, thus mak- Fio. 32.— Forces acting at any x . . . 173 inur a "hump" or crest; this in turn sinks and makes a depression or " trough"; etc. These up-and-down motions affect the neighboring portions...
e the readings must be corrected in order to give A. If the scale is made of such a material that each centimetre increases in length an amount a cm. for each degree rise in temperature, two divisions which are 1 cm. apart at 0° are a distance (l+a"0 cm. apart at t° C. Conse- quently, if the observed reading is H scale...
a line of unit length in the surface. This is a molecular force and is evidently du • to the fa.-t that a molecule in ih- a liquid is in a 184 MECHANICS different condition from one in the interior. For a surface of a given liquid in contact with a definite medium, then, no matter whether its area is large or small, t...
ust be same ; and therefore it is impossible to blow a bubble of such a liquid or to stretch a film of it on wire frames ; for it is evi- dent that, if a vertical film exists, the tension in the upper portions of the surface must be greater than in the 1< i use the former have to support the weight of the latter, and s...
o the changes. Let p and v In- the initial pressure and volume of a gas; then, if tin- temperature is kept constant and the pressure is increased top + AJP, the corresponding volume v — A v must be such that pv = (p + A/>) (v - A »•) = pv + vA/> — p\v — A/>Av. Therefore, vA/> - p&v - A/>Ay =0. l)i it if the changes are...
energy of translation. and *»ir;« Hows at once that ^ = N^i that is, that the two sets have the same number of particles in eaeh unit voln This statement when applied to gases would be: in two gases at the same pressure and temperature there are the same number of molecules in each cubic eentimetre. This •• A voLcadro...
102. — Hydraulic ram. P and Q are valves opening automatically. HYDRAULIC MACH1NX8 1 I'l'.MPs. ETC. 207 sutlii -lent to raise the valve and close it, thus stopping the flow; the valve therefore again drops owing to its weight, and the operation is repeated automatically. When the water is at rest at the beginning of th...
ts weight at any one point on tin- earth's surface; but the other properties may be changed at will. One of the simplest methods of doing this is to alter the temperature of the body; and this process will be ;>sed in the following pages. Molecular Energy. — We have proved, in the discussion of <li tins i<>n. of viscos...
and so does work, i \\'e are neglecting purposely all losses of energy by radia- tion and conduction.) In any change, then, we may write the equation : quantity of energy received by work done on the molec-nlo = increase in internal energy + work done against ex- ternal forces, such as surface pressure and gravity, or...
other, and then lowered again to the former value, has a larger volume at the end than it had at the beginning ; and this increase is not permanent, but disappears gradually after the lapse of weeks or months. This is owing to the heterogeneous character of glass ; the molecular changes produced by raising the temperat...
i.e. has the same properties in all direc- tions, this calculation is most simple. Imagine the body in the form of a cube, the length of whose edges at any one trm p. Mature tf is /, and at the temperature fa° is /3, then tin- voluin.- ;it /, ii /,:! and at tj is lf\ so the change in volume is I* — I*- It the body is n...
er, let the coefficient of cubical expansion of the solid have the value b. Then the increase in volume of the solid is v1 [1 + b (£2 — ^)] ; and hence the true change in volume of the liquid is v + vl [1. + 6(£2 — tfj)]. Experiments show that fyor nearly all liquids — water is an exception, as will be explained below ...
tually, this is not exactly true of any gas ; but this discrepancy is a consequence of the fact that Boyle's law is not exact for an actual gas urn- is the coefficient of expansion a constant.) Laws of Gay-Lussac and Charles. — The fact that all gases have approximately the same coefficient for change of pressure when ...
ts pressure is less, changes in temperature take place owing to numerous causes. We shall consider two cases of practical importance. Let a cloth with fine meshes — a piece of cheese cloth or toweling — be folded over the nozzle from which the gas is escaping ; it will expand with violence through these numerous openin...
if c is the specific heat of a body whose mass is m, and if the temperature is raised through <2 — £j degrees, the number of calories added is mc(t^ — ^). C7/.l.V(;/:> /.V 'IKMrKHATURB 251 In iron, boron, carbon, and a few other substances the specific heat varies to a marked degree at different temperatures ; and with...
ter it must be exposed to some source of heat ; if water evaporates from one's hand or from the surface of a porous jar, tin* latter is chilled, showing that heat energy has been taken from it ; as steam condenses into water in steam coils or " radiators," they are heated, showing they have received energy ; when an ac...
of the dissolved substance is precipitated; the temperature remains unchanged, and as more and more heat energy is withdrawn, equivalent amounts of solid solvent and dissolved substance separate out. This complex solid mixture is called the " cryohydrate " of the two parts. It is in equilibrium with the solution of the...
of the air and then by experiment find what temperature some solid body — like a metal can — must have in order to make moisture condense on it. This is called the " dew-point." The vapor pressure corresponding to these two temperatures is found from tables or from the curve given on page 266 : one of these expresses ...
e changed into steam ; B, when this process is finished, the pressure and temperature remaining constant; this steam can be imagined as formed directly back of the piston and exert- ing a pressure on it; so the instant marked by B is that of the " cut-off "; the steam now expands, and both temperature and pressure fall...
is performed in such a manner that compressed air at the temperature of the coil g and at about 200 Atm. flows through the inmost tube of the spiral from top to bottom, and passes out at the lower end through a valve a under a pressure of some 16 Atm., it returns upwards through the annular space between the inner and ...
pper are dissolved in dilute sulphuric acfd, 12,500 calories are absorbed. Dissociation. — One of the most interesting chemical changes is the dissoci.it inn of a '_r;ls i,,((, other gases. Thus some gases with complex molecules break down into others with simpler molecules when the temperature is raised to a high degr...
n disturbance or condition; each particle of matter makes oscillations about its centre of equilibrium, but does not move away from this as the wave itself advances ; and therefore by the " velocity of waves " is meant the distance this disturbance advances in a unit of CONVECTION, CONDUCTION, AND RADIATION 291 time. (...
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 at the extreme ends of the curves, it marks evidently tin* limiting power of the measuring instru- ment used ; ;md theref...
an imagine, moreover, a body in the vessel described above, which is entirely inclosed by some envelope which allows to pass through it waves of only one wave length ; therefore, when equilibrium is reached, the body inside must radiate as much energy in the form of waves of this wave length as it absorbs. Consequently...
t is compressed from D to C at a constant temperature ; and finally it is compressed from O to A under conditions such VOLUMES that no heat energy enters or FIG. i32.-ACarm>tcycie. leaves, and so its temperature rises to its initial value. The curves AB and CD are then " isothermals " ; AC and BD are "adiabatics." In t...
nding medium immediately in contact with it; portions affect those next them, etc. The vibrations at th< centre of disturbance must be of such a nature as to produce in tin- medium a displacement or change which can be propagated l»\ it. Thus, if the hand is moved through air or \\at.-r, <.r if a pendulum vibrate* in a...
rce are produced in the surrounding medium. The medium which carries these waves has been proved to be the same as that which carries the waves that affect our sense of sight ; namely, the "luminiferous ether." It has been proved, too, that, wherever there are variations in the electric force, there are also variations...
rcumference into a number of equal lengths so that there is a whole number included in each quadrant; from tin- i' i ids of these equal lengths drop perpendiculars upon the diameter BA\ the points thus marked off on the diam- eter correspond to equal intervals of time for the point making harmonic motion, as is evident...
; but the phases and amplitudes of these component vibrations bear relations to each other that are not the same as for the component forces. Then-Tore, die resultant complex \ibration is different from the complex force in "form." Il Is Only a harmonic force that can - reproduce " . of OOUlVe \\ ith variations in the ...
ube 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 particle of the cord, it gives the particle a motion which may be resolved into two com- ponents : uniform moti...
hore, if they are oblique to- the shore line, they will gradually turn so as to approach parallel to it, owing to the fact that in shallow water the waves are faster in the deeper portions than in the ones less so. The motion of the individual particle of a liquid as a wave passes over its surface is in general an elli...
ll in comparison with the wave length. The best method of considering the superposition is a graphical one. Thus, two plane polarized transverse waves (see page 313) which are harmonic, and whose directions of vibrations are at right angles, may be compounded as shown in Lissa- jous' figures. In particular, two such wa...
are given of these vibrating segment; (2) two vibrating segments ; tranSVCrSC vibratlOUS of (SUhree vibrating segments ; (4) superposition of •• STATIONARY MM r/>" 353 Tin- velocity of transverse waves in such a stretched flex- ible cord has been proved to be given by the formula, * d IT r=\' — , where T is the tension...
attached to a hollow box, open at one end, and of such a length that the column of air inside has the same fre- quency as the fundamental of the fork. This is called a " resonance box." An- other effect of giving the fork its peculiar shape is so to enfeeble the vibrations other than the fundamental FIG. 162. — Set of...
ven here. It may be found in Rayleigh's Theory of Sound, Vol. II, page 46. Therefore, if we know by direct experiment, or otherwise, the velocity of waves in air, we may by Kundt's method de- termine the velocity of compressional waves in any solid mate- rial out of which a rod can be made ; and then, by replacing the ...
mirrors. The law stating that the normals to the two waves and the surface lie Hl-:i-'LK< TIOH AND REFRACTION 371 in a plane was first given by the Arabian scholar Al Hazen, about 1000 A.I). 2. Refraction of Plane Waves at a Plane Surface. — Again quoting from Huygens : u In order to explain these phe- nomena on our t...
in the apparatus, O^P is the differ- ence in path from 01 and 02 to C. If it amounts to a wave length exactly, or to any integral number of wave lengths, tin- disturbances reach O in the same phase, and so the effect is great ; but, if this difference in path is exactly half a wave length, or any odd number of half wa...
one whose distance from P is 6, this will be exactly opposite in phase to disturbances reaching P at the same instant from certain points in the two emit i^mns /<>nes, tin- distances from which to P are b + - and ft — -; for. if two 2 2 waves differ by half a wave length, one produces an effect tly opposite in phase to...
easily. Let the waves come from such a direction that their wave front is tangent to the plane of the opening. Draw the line OB perpendicular to this plane, and OP oblique to it ; we shall consider the effect at various points on a screen perpendicular to OB. The effect at B depends upon the number of zones that can be...
losed volumes of air. Then by bringing them in turn near a vibrating body, he could tell by holding one of the ends of the resonator near the ear whether the par- ticular vibration that corresponded to that of the air in the resonator was present in the complex vibration of the body ; for, if it were, the corresponding...
aking small changes a pipe may be " tuned" accurately. If the pipe is not of uniform cross section, but conical, there are marked differences produced — the position of the nodes and loops is affected ; as is shown by the difference between an organ note and one produced by a horn. The action of "stops" or "pistons" in...
t. Fio. 188 a. wall. This is the explanation of "whispering galleri Similarly, in speaking tubes" ;m«l " spr.ikin<_f trumpets" the energy of the waves is «>min, .1 within certain bounds, instead of spreading out in all directions. 410 80UM) An interesting case of irregular reflection is seen in the case of air. waves p...
on applies to the har- mony of the chord consisting of the three notes of pitch 4n, 5n, and 6n. In general, two or more notes are consonant, or approximate to it. it' their pitches bear simple numerical • uch other, such as 1 : 2, 1 : 3, 2 : 3, 1 : \. - If these relations can he expressed, however, only in terms of lar...
" It will be seen, as we go on, that we can subdivide this subject in certain definite ways. Fundamental Facts Light is Due to Ether Waves. — The statement has been made before several times that light is a sensation due to waves in a medium called the ether ; but a brief summary of the facts on which this is based may...

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