Page:Elementary Text-book of Physics (Anthony, 1897).djvu/176

163 The formula for velocity then becomes $$V = \sqrt{\frac{\gamma P}{d_{0}}(1 + \alpha t)}.$$ This formula shows that the velocity at any temperature is the velocity at 0° multiplied by the square root of the factor of expansion.

136. Measurements of the Velocity of Sound.—The velocity of sound in air has been measured by observing the time required for the report of a gun to travel a known distance.

One of the best determinations was that made in Holland in 1833. Guns were fired alternately at two stations about nine miles apart. Observers at one station observed the time of seeing the flash and hearing the report from the other. The guns being fired alternately, and the sound travelling in opposite directions, the effect of wind was eliminated in the mean of the results at the two stations. It is possible, by causing the sound-wave to act upon diaphragms, to make it record its own time of departure and arrival, and by making use of some of the methods of estimating very small intervals of time the velocity of sound may be measured by experiments conducted within the limits of an ordinary building.

The velocity of sound in water was determined on Lake Geneva in 1836 by an experiment analogous to that by which the velocity in air was determined.

In § 144 and § 146 it is shown that the time of one vibration of any body vibrating longitudinally is the time required for a sound-wave to travel twice the distance between two nodes. The velocity may, therefore, be measured by determining the number of vibrations per second of the sound emitted, and measuring the distance between the nodes.

In an open organ-pipe, or a rod free at both ends, when the fundamental tone is sounded the sound travels twice the length of the rod or pipe during the time of one complete vibration. If rods of different materials be cut to such lengths that they all give the same fundamental tone when vibrating longitudinally, the ratio of their lengths will be that of the velocity of sound in them.

In Kundt's experiment, the end of a rod having a light disk attached is inserted in a glass tube containing a light powder strewn