CHAPTER VI.

ACOUSTICS.

SECTION I.

PRODUCTION AND PROPAGATION OF SOUND.

206. Acoustics is that branch of Physics which treats of the laws of generation and propagation of sound.

207. Sound is a motion of matter capable of affecting the ear with a sensation peculiar to that organ.

Sound is caused by the vibration of some body, and is transmitted by successive vibrations to the ear. The original vibrating body is said to be sonorous. A body which transmits sound is called a medium. The principal medium of sound is the atmosphere; but all elastic bodies transmit sound, and are, therefore, media.

Let us take, for illustration, a stretched cord which is made to vibrate by a bow, as in a violin, for example. When the cord is drawn from its position of rest, a cb (Fig. 151), to the position, a db, every point of the cord is drawn from its position of equilibrium; when it is let go, its elasticity causes it to spring back to its original position. In returning to this position, it does so with a velocity that carries it past a cb to a eb, from which it returns again nearly to ad b, and so on vibrating backward and forward, until, after a great number of oscillations, it at length comes to rest.

208. Sound-Waves in Air.-Mode of Propagation. Sound-waves are produced in the air by the vibration of some sonorous body. When the body moves forward, it strikes the air in front of it, and condenses a stratum whose thickness depends on the rapidity of vibration; the particles of this stratum impart the condensation to those of the next, and these in turn to those of the next, and so on; the condensation thus transmitted outward is called the condensed pulse. When the body moves backward, the air in front of it follows, and produces rarefaction in a stratum whose thickness depends on the rapidity of vibration; this causes a backward movement and consequent rarefaction in the next stratum, which is transmitted to the next, and so on; the rarefaction thus propagated outward is called the rarefied pulse.

Fig. 152 illustrates the formation of sound-waves by the vibrations of a tuning-fork. The prong, a, as it springs outward, condenses the air in front, and then, receding, leaves behind it a partial vacuum. Thus each complete vibration generates a condensed and a rarefied pulse, and these together constitute a sound-wave. The dark spaces, a, b, c, d, represent the condensations, and the lighter spaces, a', b, c, d', the rarefactions; the wave-lengths are the distances a b, bc, cd.

When a bell is rung, the air around it is set in motion, and soundwaves are generated, which move outward in every direction in the form of spherical shells, as shown in Fig. 153.

The rate at which the sound-wave travels is the velocity of sound; the distance through which it travels in the time of one

vibration of the sonorous body is the wave-length.

The form of the

sound-wave is transmitted through the air, but the individual particles of air simply oscillate to and fro in the direction of wave propagation, moving forward on the passage of the condensed and backward on the passage of the rarefied pulse; the distance through which each particle oscillates is called the amplitude of vibration of the particle.

Any two particles situated on a line in the direction of propagation, and at a distance from each other equal to a wave-length, are always moving in the same direction and with equal velocities; such particles are said to be in the same phase. All the particles of any wave that are in the same phase are on the surface of a sphere, which is called a wave-front.

209. Combinations of Sound-Waves. Many sounds may be transmitted through the air at the same time, and in some cases there is no perceptible interference of the soundwaves. In listening to a concert of instruments a practised ear can detect the particular sound of each instrument.

Sometimes, however, an intense sound covers up or drowns a more feeble one; thus, the sound of a drum might drown that of the human voice. Sometimes feeble sounds, which are too faint to be heard separately, by their union produce a sort of murmur. Such is the cause of the murmur of waves, the rustling sound of a breeze playing through the leaves of a forest, and the indistinct hum of a distant city.

210. Coincidence and Interference of SoundWaves. - Two sets of sound-waves may coincide so as to increase the intensity of the sound, or they may interfere so as to neutralize each other and produce silence:

Suppose we have two tuning-forks, A and B, which produce waves of exactly the same length. Let them be placed a wavelength apart, as shown in Fig. 154. The two sets of vibrations

B

A

C

Fig. 154.

will coincide, and the intensity of the sound will be greater than if one were vibrating alone. The same would evidently occur if the distance between it and B were any number of whole wavelengths.

But suppose A and B to be only half a wave-length apart. It is evident that the rarefactions of one of the systems of waves will then

B A

Fig. 155.

coincide with the condensations of the other system, and the result will be interference, by which both systems of waves will be destroyed. This result is indicated by the uniformity of shading in Fig. 155.

The interference of sound-waves can be shown by striking a small tuning-fork, and then holding it a short distance from the ear, rolling the stem at the same time between the thumb and finger. We shall find several positions where the sound-waves neutralize one another and no sound is heard, and also several where the waves coincide and there is a reinforcement of sound.

211. Beats.—When two tuning-forks which are not quite in unison are sounded together, there is no continuous sound produced, but a peculiar, palpitating effect, which is owing to a series of alternate reinforcements and diminutions of the sound. This succession of sounds with the intervals of comparative silence is known to musicians by the name of beats, and is the result of the coincidence and interference of the sound-waves.

Suppose one of the forks vibrates 100 times in a second, and the other 101 times. If the waves start at the same moment the condensations will coincide and also the rarefactions, but they begin to interfere more and more, inasmuch as one system has been gradually falling behind the other, until at the middle of the second it will have amounted to half a wave-length, and the two sounds will destroy each other.

At the end of the second, when one fork has completed its 100th vibration and the other its 101st, one system has fallen behind the other one wave-length, and there is coincidence again of crest and depression, and the full effect of both sounds reaches the ear. We have, then, one beat and one interval in every second.

In general, beats are produced by two musical sounds of nearly the same pitch emitted at the same time. The number of beats per second is equal to the difference of the rates of vibration.

Beats are frequently heard in the sound of church bells, and in the lower octaves of large organs. Telegraph wires, when made to vibrate by a strong wind, produce beats. These can be observed by pressing one ear against a telegraph-post and closing the other. If we strike simultaneously one of the lower white keys of a piano and the adjacent black key, beats will be heard.

Beats are of great value in tuning musical instruments. The notes given out by two musical instruments of slight difference in pitch can be brought into unison by tuning until the beats disappear.

212. Sound is not propagated in a Vacuum. — That some medium is necessary for the transmission of sound may be shown by the following experiment.

A bell is placed under the receiver of an air-pump, provided with a striking apparatus set in motion by clock-work. Before