Page:Elementary Text-book of Physics (Anthony, 1897).djvu/164

150 flame in a mirror which is turned from side to side, while the flame is quiescent, it appears drawn out into a broad band of light, but when it is agitated by a sound near it, it appears serrate on its upper edge or even as a series of separate flames. This lengthening and shortening of the flame is evidence of a to-and-fro movement of the membrane, and hence of the sounding body that gave rise to the movement. If a hole be made in the side of an organ-pipe and the capsule made to cover it, the vibrations of the air-column within the pipe may be shown. By suitable devices the vibratory motion of all sounding bodies may be demonstrated.

129. Propagation of Sound.—The vibratory motion of a sounding body is ordinarily transmitted to the ear through the air. This is proved by placing a sounding body under the receiver of an air-pump and exhausting the air. The sound becomes fainter and fainter as the exhaustion proceeds, and finally becomes inaudible if the vacuum is good. Sound may, however, be transmitted by any elastic body.

In order to study the character of the motion by which sound is propagated, let us suppose $$AB$$ (Fig. 43) to represent a cylinder of some elastic substance, and suppose the layer of particles a to suffer a small displacement to the right. The effect of this displacement is not immediately to move forward the succeeding layers, but $$a$$ approaches $$b$$, producing a condensation, and developing a force that soon moves $$b$$ forward; this in turn moves forward the next layer, and so the motion is transmitted from layer to layer through the cylinder with a velocity that depends upon the elasticity (§ 103) of the substance, and upon its density. This velocity is expressed by the formula $$V = \sqrt{\frac{E}{D}}$$, in which $$E$$ represents the elasticity of the substance, and $$D$$ its density (§ 134). Now, if we