the instant of discharge of a pistol was recorded electrically on the rotating drum of a chronograph, while the arrival of the sound at the distant station, where it caused a thin stretched membrane to vibrate, was electrically recorded on the same drum. By these experiments he found that the velocity was influenced by the size of the pipes to a small extent, and also that very intense sounds traveled slightly faster than feebler ones. He also conducted experiments in the open air, using the same recording apparatus, and found the velocity of sound in dry air at 0° C. to be 330.6 meters per second.

Bosscha determined the velocity of sound by causing two little hammers to give simultaneous taps at regular intervals, the frequency of the taps being determined by a pendulum which made electrical connections at every swing. If one of the sounding instruments is placed beside the observer while the other is moved away, the taps are no longer heard simultaneously, but those from the more distant one come later; if moved far enough apart so that the sound from the tap of the distant hammer reaches the ear at the same instant as the next succeeding tap of the nearer hammer, the two are again heard simultaneously, and the distance between the two sounders divided by the time. interval between the taps gives the velocity of sound.

288. Velocity of Sound in Water and in Solids and Gases. -Colladon and Sturm measured the velocity of sound in the water of Lake Geneva by causing a bell to sound under water and using as a receiving instrument a sort of ear trumpet with the outer end closed by a rubber diaphragm and placed beneath the surface of the lake. The velocity was found to be 1435 meters per second. In solids the velocity of sound is usually measured by the longitudinal vibrations of rods or wires as explained later, §342.

The velocity of sound in various gases and vapors has been determined by comparison with that in air by the method of Kundt, $335.

The velocities of sound in some common media are given in the following table. The velocity of sound in wood and steel is so great that a person standing near one end of a long beam or rail that is struck at the farther end hears two sounds in quick succession, first that transmitted by the solid and then that through air.

289. Velocity of Compressional Waves.-The velocity of a compressional wave in air may be readily calculated by Newton's formula

It was shown by Newton that the elasticity of a gas at constant temperature is equal to its pressure (see $242). But on substituting pressure for elasticity in the above formula the calculated velocity was found to be too small.

Laplace pointed out that though the average temperature of air is not changed by the passage of sound waves, yet in the compressed part of a wave the air is heated for the instant, and where it is rarefied there is cooling, and that these changes take place so rapidly that there is no time for heat to flow from one part to another, so that the air is practically in an adiabatic condition, ($242). The effect of heating during compression is to resist the compression, and cooling during expansion acts to oppose the expansion, the effective elasticity in this case is therefore increased and in case of air has been found to be 1.40 times as great as if the temperature had remained constant. The formula thus becomes for a gas like air,

Substituting the values for air at normal temperature and pressure, and expressing both pressure and density in C. G. S. units, we have

V=

76. X 13.6 X 980. X 1.40
.001293

=33120. cms. per sec.,

which is in good agreement with the velocity of sound as found by experiment.

In case also of solids and liquids the results obtained by the formula agree with velocities obtained by direct experiment. The elasticities of these substances are so much greater than that of air that the velocities of sound in them are large in spite of their great densities.

Thus in water the elasticity or ratio of pressure increase to corresponding decrease in volume is, in C. G. S. units,

76. X 13.6 X 980
.000047

2. 16 X 1010 dynes per sq. cm.

or 15230 times that of air, while it has only 773 times the density of air.

290. Influence of Temperature and Pressure on Sound Velocity in Air. From the formula in the preceding paragraph it is clear that the velocity of sound in air is independent of the pressure, for when the pressure is increased the density increases in Ρ

the same proportion, by Boyle's law, and the ratio remains d

constant, and consequently the velocity is constant so long as the temperature is not changed.

But if the temperature is raised, pressure being constant, the

density diminishes and the ratio increases. Hence the velocity

p d

of sound in air is increased, or about 2 ft. or 0.60 meter per second per degree C. rise in temperature.

291. Influence of Pitch on Velocity of Sound.-It may be easily noticed that the notes of music coming from a distant band are heard in the same relation to each other as if the band were near. There is no confusion of the melody such as would result if high-pitched sounds traveled faster or slower than low ones. Regnault made careful observations on this point

and concluded that the velocity of sound is the same whatever the pitch may be.

It will be shown later that the pitch of a sound depends upon wave length, hence we conclude that the velocity of sound is the same for all wave lengths.

REFLECTION AND REFRACTION OF WAVES.

292. Reflection of Water Waves.-When a water wave meets an immovable obstacle it is turned back or reflected. Since the obstacle does not move, it cannot receive energy from the incident wave, and therefore the reflected wave carries the energy away. Each point of the obstacle reacts against the waves which meet it and so produces a periodic disturbance and may be regarded as a center from which waves are sent out. The reflected wave as a whole is the resultant of these little waves coming from each point of the obstacle.

Suppose a wave from a center O, figure 161, meets a straight wall BC. When in the position AED the disturbance has just

FIG. 161. Reflection of waves.

reached the wall at E and is about starting back. By the time the wave at A has advanced to B and at D has reached C, the part of the wave reflected at E will have returned an equal distance to F.

If the wall had not been there the wave would have advanced to the position of the dotted line BGC, but since after reflection it has the same velocity as before, the reflected wave will at each point have gone back from the wall as far as it would have passed the line BC if the wall had not been there. The front of the returning wave BFC has therefore the same curvature as BGC if the wall is flat. The returning wave is therefore circular having its center at a point O' which is as far back of the wall as the center O is in front of it; and the line OO' is at right angles to the wall.

Another method of looking at this subject is interesting. The effect of the vertical wall is to oppose any forward or backward motion

of the water particles next to it without interfering with vertical motions. Let us now imagine the wall removed and that whenever a wave starts from O an exactly equal wave sets out from O'. The waves will meet along the line BC and the forward or backward movement due to the one will be exactly balanced by that of the other, while their vertical movements will be added. There results, therefore, an up-and-down oscillation along the line BC exactly as if the wall were there.

On each side of the line BC there will be waves coming toward the line and others going back from it exactly as if reflected from it. And indeed they may be properly regarded as reflected, for there is no transfer of energy across the line BC because there is no forward or backward motion across that line, and if a thin wall were slipped in along BC separating the two systems of waves the motion would not be changed on either side.

1

2

W

FIG. 162.

293. Angle of Reflection.-When a wave front meets a reflecting surface obliquely, the direction of the wave front and its direction of propagation are changed as shown in figure 162. At W is shown a portion of a wave front. approaching P where it is reflected, afterward advancing as shown at W2 as if it came from O'. The angle i between the direction of advance of the incident wave and the normal to the surface is called the angle of incidence, while the angle r between the direction in which the reflected wave moves and the normal N is called the angle of reflection. The angle of reflection is equal to the angle of incidence. For the angles a and b are clearly equal and the angle i is equal toa, and r is equal to b, since the lines OO' and NP are parallel. It is interesting to see how the reflected wave may be regarded as the resultant of little waves coming back from each point of the reflecting surface. Let AB (Fig. 163) be a wave front meeting the reflecting surface AC at A. The disturbance at just A causes a little circular wave to go back which will have a radius AD equal to BC by the time that the wave front at B has reached C, since the velocity of the returning wave is the same as that of the advancing one. So also the circular wavelet starting backward from F when the advancing wave has reached