waves travel faster because gravitation force predominates, while in shorter waves surface tension has the principal effect.

COMPRESSIONAL WAVES.

280. Compressional Waves.-Water waves of the type just considered are surface waves, and can only exist at the surface of a medium. But the kind of wave now to be studied can travel in every direction through an elastic medium.

Consider the model shown in figure 156, which represents a series of equal masses resting in a frictionless groove and connected by springs. If the first mass is moved toward the second, the latter will move because the spring between the two is compressed. But it will not begin to move until after the first mass has approached it; for if the two moved exactly together

ототот

FIG. 156.-Illustrating elasticity and inertia of medium.

there would be no compression of the spring between them, and consequently no force exerted on the second mass to move it. As the

second mass moves forward there is compression of the second spring, followed by motion of the third mass, and so on, the masses being set in motion one after the other as the wave of compression reaches spring after spring.

So also if the first mass is drawn away from the others, the first spring is stretched, causing motion of the second mass which stretches the second spring. The motion is therefore communicated through the whole series as a wave accompanied by stretching or expansion of the springs.

Such a wave of expansion or compression is set up whenever a material object is set in motion or brought to rest; for all bodies may be considered as made up of massive particles in elastic equilibrium with each other, like the balls and springs in the diagram. Thus, when a chair is lifted, a wave of expansion runs down through it, and when it is set on the floor a wave of compression runs up.

281. Newton's Formula for Velocity of a Compressional Wave. -The velocity of such a wave depends on the elasticity and density of the medium. Recurring to the illustration, it is evident that making the springs between the balls stiffer will increase the speed with which the motion will be communicated

from one ball to the next, while if the masses of the balls are made greater the effect will be to make the speed of the wave less.

It was proved by Newton from the principles of mechanics that the velocity of a wave of compression or expansion in a medium of which the volume elasticity is e and the density d is expressed by the formula,

282. Motion in a Series of Compressional Waves.-If the first of the series of balls represented in figure 156 is made to oscillate regularly backward and forward, now moving toward the second ball and now away from it, a series of waves will be sent along the row of balls, alternately waves of compression and expansion; and each ball will oscillate just as the first one does, though the second will always be in a phase of motion a little behind the first, the third will lag behind the second and so on. This is precisely the kind of motion which is set up in air by a tuning-fork or other rapidly vibrating body, and which excites in our ears the sensation of sound. Such waves in air are accordingly known as sound waves.

The details of the motion in a sound wave may be understood from figure 157.

The diagram illustrates the relative phases of motion of a series of particles in the wave one-eighth of a wave length apart. Each particle is shown as a black dot on a short straight line which represents the path in which it oscillates, the center of the line being its equilibrium position. Suppose the first particle is made to oscillate in simple harmonic motion, then that will be the mode of vibration of all the particles, and each will move back and forward keeping vertically under an imaginary companion particle that is supposed to move with uniform velocity around in the corresponding circle shown in the diagram.

It will be seen from the positions of the companion particles in the circles that, taken in the order in which they are numbered, each is one-eighth of a complete vibration behind the phase of the preceding particle; indeed, the associated circles are only used to show the relative phases of the numbered particles below, which represent actual particles in the medium.

Particle 1 is at the end of its path, while the second particle is moving toward the end and will be there an eighth of a period later, when 3 will be in the phase now shown by 2, and so on; therefore the wave will have moved forward in the direction of the long arrow underneath. It will be seen that particles 1 and 9 are in the same phase, and accordingly the distance between them is the wave length. The particle at 7 is in the center of a condensed region, where the particles are closer together than normal, while those at 3 and 11 are the centers of rarefied or expanded regions. In the condensed region the particles are moving forward in the direction in which the wave is advancing; in the rarefied region they are moving opposite to the wave. There are intermediate points where the medium is neither condensed nor rarefied where the particles are for the instant at rest at the end of their paths of vibration, as at 1, 5, and 9.

+

R

C

FIG. 158.-Motion of air layers in sound wave.

R

It must not be forgotten that each of the particles considered is only one of a layer all vibrating in the same way. This is represented in figure 158, where the dots of the previous diagram are replaced by heavy lines which represent successive layers of particles, differing in phase by one eighth of a period. The small arrows indicate the velocities of the layers at the given instant, and the instantaneous position of the regions of condensation. and rarefaction are marked by the letters C and R, respectively.

To sum up, in a compressional wave the particles vibrate longitudinally, or back and forth in the direction of advance of the wave, and there is a progressive change in phase, in con

sequence of which alternate regions of compression and rarefaction are produced.

The amplitude in such a wave is the distance that a particle oscillates on each side of its equilibrium position, or half the whole distance through which it vibrates.

283. Illustration. The propagation of a wave of compression or rarefaction may be very well shown in a regular spring a meter and a half long which is supported by threads in a

horizontal position, as shown in figure 159. The turns of the spring should be rather large and it should be of such a stiffness that a wave will take a second or two to travel its length.

SOUND.

284. Sound Communicated by Waves.-There are three principal evidences that sound is communicated by compressional waves through material bodies. First, sound is not communicated through a vacuum; second, the motions of sounding bodies are such as might be expected to set up compressional waves; and, third, the observed velocity of sound is the same as that of compressional waves, both in air and in other media.

285. Sound Requires a Material Medium.-Place an alarm bell rung by clockwork under the receiver of an air pump, as in figure 160, so that it may rest on a mass of soft cotton, or is otherwise supported so that no vibrations can be transmitted through its supports to the plate of the air pump. When the

air is exhausted from the receiver the bell is no longer heard, however vigorously it may be ringing. Sound waves, therefore, do not pass through a vacuum, they require a material medium.

286. Sound Originates in Vibrating Bodies.-All sources of sound are vibrating bodies capable of setting up air vibrations. A brass plate supported at the centre and covered with sand if set in vibration by a bow may be made to sound in a variety of different ways, but in each case there is a characteristic arrangement of the sand showing that

FIG. 160.-Bell in vacuo.

a particular mode of vibration of the plate corresponds to each sound. (See Fig. 198.) Tuning-forks are set in vibration by being struck, strings by being bowed, the vibrations of the string being evident to the eye or causing a buzzing sound when the string is touched with a piece of paper. In reed instruments the metal tongue of the reed vibrates strongly when sounding, and even in flutes and organ pipes it may easily be shown that the air is set in strong vibration.

287. Velocity of Sound. The velocity of sound in air was determined by two Dutch observers, Moll and Van Beck, in 1823, by timing the interval between seeing the flash of the discharge of a distant cannon and hearing its report.

Cannons were set up on two hills nearly 11 miles apart, and by observing alternately first from one hill and then from the other the observers sought to eliminate the influence of any air currents which might exist. At the same time the temperature of the air was observed at a number of points between the two stations. The velocity was thus found to be 1093 ft. or 333 meters per sec. at 0° C.

Regnault (1810-1878) conducted an extensive series of investigations on the velocity of sound in the Paris water mains, which afforded large tubes free from wind disturbance and at a uniform temperature. He made use of an automatic apparatus by which