380. Mechanism of transmission. When a firecracker or toy cap explodes, the powder is suddenly changed to a gas, the volume of which is enormously greater than the volume of the powder. The air is therefore suddenly pushed back in all directions from the center of the explosion. This means that the air particles which lie about this center are given violent outward velocities.* When these outwardly impelled air particles collide with other particles, they give up their outward motion to these second particles, and these in turn pass it on to others, etc. It is clear, therefore, that the motion started by the explosion must travel on from particle to particle to an indefinite distance from the center of the explosion. Furthermore, it is also clear that, although the motion travels on to great distances, the individual particles do not move far from their original positions; for it is easy to show experimentally that whenever an elastic body in motion collides with another similar body at rest, the colliding body simply transfers its motion to the body at rest and comes itself to rest.

FIG. 342. Illustrating the propagation of sound from particle to particle

Let six or eight equal steel balls be hung from cords in the manner shown in Fig. 342. First let all of the balls but two adjacent ones be held to one side, and let one of these two be raised and allowed to fall against the other. The first ball will be found to lose its motion in the collision, and the second will be found to rise to practically the same height as that from which the first fell. Next let all of the balls be placed in line and the end one raised and allowed to fall as before. The motion will be transmitted from ball to ball, each giving up the whole of its motion practically as soon as it receives it, and the last ball will move on alone with the velocity which the first ball originally had.

* These outward velocities are simply superposed upon the velocities of agitation which the molecules already have on account of their temperature. For our present purpose we may ignore entirely the existence of these latter velocities and treat the particles as though they were at rest, save for the velocities imparted by the explosion.

The preceding experiment furnishes a very nice mechanical illustration of the manner in which the air particles which receive motions from an exploding firecracker or a vibrating tuning fork transmit these motions in all directions to neighboring layers of air, these in turn to the next adjoining layers, etc., until the motion has traveled to very great distances, although the individual particles themselves move only very minute distances. When a motion of this sort, transmitted by air particles, reaches the drum of the ear, it produces the sensation which we call sound.

ABC

Wave length

381. A train of waves; wave length. In the preceding paragraphs we have confined attention to a single pulse traveling out from a center of explosion. Let us next consider the sort of disturbance which is set up in the air by a continuously vibrating body, like the prong of Fig. 343. Each time that this prong moves to the right it sends out a pulse which travels through the air at the rate of 1100 feet per second, in exactly the manner described in the preceding paragraphs. Hence, if the prong is vibrating uniformly, we shall have a continuous succession of pulses following each other through the air at exactly equal intervals. Suppose, for example, that the prong makes 110 complete vibrations per second. Then at the end of one second the first pulse sent out will have reached a distance of 1100 feet. Between this point and the prong there will be 110 pulses distributed at equal intervals; that is, each two adjacent pulses will be just 10 feet apart. If the prong made 220 vibrations per second, the distance between adjacent pulses would be 5 feet, etc. The distance between two adjacent pulses in such a train of waves is called a wave length.

FIG. 343. Vibrating reed sending out a train of equidistant pulses

382. Relation between velocity, wave length, and number of vibrations per second. If n represents the number of vibrations per second of a source of sound, 7 the wave length, and v the velocity with which the sound travels through the medium, it is evident from the example of the preceding paragraph that the following relation exists between these three quantities: (1)

l=v/n, or v = nl ;

that is, wave length is equal to velocity divided by the number of vibrations per second, or velocity is equal to the number of vibrations per second times the wave length.

383. Condensations and rarefactions. Thus far, for the sake of simplicity, we have considered a train of waves as a series of thin, detached pulses separated by equal intervals of air at rest. In point of fact, however, the air in front of the prong B (Fig. 343) is being pushed forward not at one particular

ABC

d

α

+

FIG. 344. Illustrating motions of air particles in one complete sound wave consisting of a condensation and a rarefaction

instant only but during all the time that the prong is moving from A to C, that is, through the time of one-half vibration of the fork; and during all this time this forward motion is being transmitted to layers of air which are farther and farther away from the prong, so that when the latter reaches C, all the air between C and some point c (Fig. 344) one-half wave length away is crowding forward and is therefore in a state of compression, or condensation. Again, as the prong moves back from C to A, since it tends to leave a vacuum behind it, the adjacent layer of air rushes in to fill up this space, the layer next adjoining follows, etc., so that when the prong reaches A, all the air between A and c (Fig. 344) is moving backward and

is therefore in a state of diminished density, or rarefaction. During this time the preceding forward motion has advanced one half wave length to the right, so that it now occupies the region between e and a (Fig. 344). Hence at the end of one complete vibration of the prong we may divide the air between it and a point one wave length away into two portions, one a region of condensation ac, and the other a region of rarefaction ca. The arrows in Fig. 344 rep

resent the direction and relative magnitudes of the motions of the air particles in various portions of a complete wave.

At the end of n vibrations the first disturbance will have reached a distance n wave lengths from the fork, and each wave between this point and the fork will consist of a condensation and a rarefaction, so that sound waves may be said to consist of a series of condensations and rarefactions following one another through the air in the manner shown in Fig. 345.

Wave length may now be more accurately defined as the distance between two successive points of maximum condensation (b and f, Fig. 345) or of maximum rarefaction (d and h).

384. Water-wave analogy. Condensations and rarefactions of sound waves are exactly analogous to the familiar crests and troughs of water waves.

FIG. 346. Illustrating wave length of

water waves

Thus, the wave length of such a series of waves as that shown in Fig. 346 is defined as the distance bf between two crests, or the distance dh, or ae, or cg, or mn, between any two points which are in the same condition, or phase, of disturbance. The crests (that is, the shaded portions, which are above the natural level of the water) correspond exactly

to the condensations of sound waves (that is, to the portions of air which are above the natural density). The troughs (that is, the dotted portions) correspond to the rarefactions of sound waves (that is, to the portions of air which are below the natural density). But the analogy breaks down at one point, for in water waves the motion of the particles is transverse to the direction of propagation, while in sound waves, as shown in §383, the particles move back and forth in the line of propagation of the wave. Water waves are therefore called transverse waves, while sound waves in air are called longitudinal waves. 385. Distinction between musical sounds and noises. current of air from a 1-inch nozzle be directed against a row of forty-eight equidistant 4-inch holes in a metal or cardboard disk, mounted as in Fig. 347 and set into rotation either by hand or by an electric motor. A very distinct musical tone will be produced. Then let the jet of air be directed - against a second row of forty-eight holes, which differs from the first only in that the holes are irregularly instead of regularly spaced about the circumference of the disk. The musical character of the tone will altogether disappear.

The experiment furnishes a very striking illustration of the difference between a musical sound and a noise.

Let a

pulses the condition for

a musical tone

Only those sounds possess a musical qual- FIG. 347. Regularity of ity which come from sources capable of sending out pulses, or waves, at absolutely regular intervals. Therefore it is only sounds possessing a musical quality which may be said to have wave lengths.

386. Pitch. While the apparatus of the preceding experiment is rotating at constant speed, let a current of air be directed first against the outside row of regularly spaced holes and then suddenly turned against the inside row, which is also regularly spaced but which contains a smaller number of holes. The note produced in the second case will