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second. The velocity at any temperature, in meters per second, may be found by substituting the reading of the Centigrade thermometer for t in the following formula:

v = 332.4 V1 + .003665 t.


EXAMPLE. - Find the velocity of sound when the thermometer reads 26° Centigrade.

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If the distance is required in feet, it can be found by substituting 1090.5 for 332.4 in Formula 41.

For approximate calculations the increase in velocity due to a rise in the temperature may be taken as 0.6 m. or 2 ft. per degree Centigrade, and 0.33 m. or 1.1 ft. per degree Fahrenheit. For most purposes the approximate results are sufficiently accurate.

199. The Velocity of Sound in Any Medium is directly proportional to the square root of the elasticity of the medium, and inversely proportional to the square root of its density. By using a proper numerical value for elasticity (Formula 1), the velocity of sound can be calculated from the equation

v = V



The velocity of sound in air is increased by a rise in temperature, chiefly because heat causes air to expand, and thus decreases its density.

200. The Velocity of Sound in Liquids varies according to the above law. The velocity of sound in water has been measured directly in much the same way as the velocity in

air. A bell was struck under water in the Lake of Geneva, and a quantity of powder was fired at the same instant. An observer, at a station 8 miles away, measured the time that elapsed between the flash and the instant when the sound of the bell was received through the water. The velocity was found to be 4.3 times the velocity in air. Not only is the velocity greater in water than in air, but sounds are transmitted more distinctly. This fact is made use of by submarine boats in communicating with ships and other submarines, by under-water signals.

201. The Velocity of Sound in Solids is so great that in measuring it directly the stations must be far apart. Measurements have been made, however, and the velocity in copper has been found to be about 11.1 times as great as in air, and in steel wire 15 times as great.

If the ear is placed close to a long wire, or to a rail of a railroad, a blow struck upon the wire or rail at a distance will be heard twice, first through the solid, and then again through the air.

202. The Reflection of Sound. In the first demonstration in § 196 the longitudinal wave sent along the spring is reflected from the fixed end. Sound vibrations are reflected in a similar manner. The law of reflected motion (§ 65) holds true for reflected sound. A good illustration of reflected sound is obtained by standing in a circular archway with the head in the center of curvature of the arch, and making a slight hissing sound. The sound will be reflected to the ear from all points of the arch and will be much increased in volume.

203. Echoes. The repetition of a sound through reflection from any surface is called an echo. The distinctness

of the echo depends upon how fully the sound is reflected, while the length of the sound that can be repeated depends upon the distance of the reflecting surface. If it takes one second to pronounce a word, and if the speaker hears the echo as soon as the word is pronounced, his distance from the reflecting surface is about 166.2 m. (one half of 332.4 m.), since in that case the sound must go from the speaker to the reflecting surface and back in one second. If a single syllable is pronounced in one fifth of a second, the surface must be at least 33.24 m. away to produce a distinct echo. There are several noted examples of echoes in the hall underneath the dome of the capitol in Washington.

204. Multiple Echoes. When a sound is made between two parallel cliffs, the echo may be repeated many times, thus forming a multiple echo. Two stones sharply struck together between two parallel buildings will produce a rattling sound like hail, if the buildings are the right distance apart (about 50 feet). A cornet, sounded in a deep valley between steep hills, will give rise to a series of musical echoes that gradually decrease in intensity and finally cease.


1. What is a simple harmonic motion?

2. What is the difference between a longitudinal and a transverse vibration?

3. Define wave length.

4. Is every vibrating body a sounding body? Explain.

5. Why is sound carried more rapidly by solids than by gases? 6. Why does sound travel in air more rapidly when the temperature rises?

7. When the wind blows over a field of grain a series of waves is set up. Describe the motion of the waves and of the heads of grain.

8. What would be the wave length in Fig. 187 if the distance between particles 1 and 7 were 8 ft.?


9. Let L the wave length of a given sound, N the number of vibrations per second, and v the velocity per second. Write three equations, giving the value of each element in terms of the other two. 10. How do fishes hear?

11. Why is it sometimes difficult for a good speaker to be heard in a public hall?

12. How may the difficulty be partially removed?


1. What is the velocity of sound in air when the temperature is 23° C.?

2. How great a distance will the sound of a whistle go in 3 seconds when the temperature is 20° C.?

3. A man is seen chopping wood and the sound of the blow is heard one half second after the ax is seen to strike. How far away is the wood chopper if the temperature is 14° C.?

4. A mail tube in a certain city became clogged and a pistol was fired at the open end of the tube. The report came back from the obstruction 1 seconds afterward. How far from the open end was the pipe stopped, the temperature being 18° C.?

5. How long after a blast is set off in a quarry will the report be heard at a point 8500 ft. distant, the temperature being 22° C.? 6. The smoke from an exploding bomb used in day fireworks was observed, and after an interval of 9.4 seconds the report was heard. What was the distance, the temperature being 24° C.?

7. Five seconds elapsed between the firing of a gun and its echo from a cliff. What was the distance of the cliff, the thermometer reading 20° C.?

8. A blow, struck with a hammer on the rail of a railroad, was heard through the rail in one fifth of a second, and then through the air 2.8 seconds later. The temperature was 18° C. How far away was the blow struck? What was the velocity of sound in the rail? 9. The report of the explosion of a submarine mine 10 miles away was heard through the water in 11 seconds. How many times greater was the velocity in the water than that in the air at 12° C.? 10. Thunder is heard just 11 seconds after the lightning flash is seen. The temperature being 23° C., what was the distance?


205. Interference in Wave Motion. -Demonstration. - Repeat the demonstration of § 189, showing a transverse wave set up in a wire spring by a light blow. Just when the wave is reflected from the fixed end of the coil, strike a second blow: the direct and reflected waves will meet, and there will be some one part of the spring where the tendency of one wave to raise the spring will be exactly balanced by the tendency of the other wave to lower it.

This effect is called interference. Interference is a phenomenon attendant upon all wave motion, and arises from the fact that a medium that will transmit one wave motion will also transmit others at the same time. If the resultant of all the forces acting upon a particle at any

time is zero, the result will be no motion, or interference. Interference in sound waves produces silence.

Demonstration.-Sound a tuning fork, pref— erably one with a sounding box, as in Fig. 188, and move it rapidly toward, and then away from, a smooth wall.

FIG. 189


FIG. 188

Observe the interferences that take place.

206. Resonance. When two waves act in the same direction upon a particle, they cause it to vibrate with greater amplitude. The resulting amplitude is the sum of the amplitudes of two waves. Such an effect in sound waves gives rise to a reënforcement of the sound, called


Demonstration. - Fill a tall glass jar nearly full of water, and get a piece of large glass tubing about a foot long, or the chimney of a student lamp. Hold a sounding

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