used raises one ton 20 ft. in one minute, what fraction of the total heat-energy developed does it use?

16. How many pounds of steam at 100° will be produced from water at 100° by the combustion of 2 lbs. of coal? (See Prob. 13.)

17. A man whose weight is 150 lbs. walks up a staircase 20 ft. high. How much heat-energy does he expend in doing so?

CHAPTER IX.

SOUND.

DEFINITIONS.-Sound; wave; medium; vibration; condensation and rarefaction; period; wave-length; intensity; amplitude; pitch; fundamental; harmonic; overtone; timbre; resonance; beats.

XLII. VELOCITY OF SOUND.

NOTE.-The velocity of sound in air at 0° may be taken as 332 m., or 1090 ft. per second.

1. How long will sound take to traverse a distance of 2 kilometers?

2. A gun is fired at a certain distance from an observer. He finds that 4.1 seconds elapse between the flash and the report. Regarding the velocity of light for short distances as practically infinite, how far away is the gun from the observer?

3. How may the distance of the place where a "flash of lightning" occurs be found by observing the interval between the flash and the thunder following? Find how many miles may be estimated for each second of the interval.

4. A person standing in front of a cliff finds that 1.2 seconds elapse between a shout and its echo from the cliff. How far is he from the cliff?

NOTE.

For every degree (Centigrade) rise of temperature above 0° the velocity of sound in air increases about .6 m., or 2 ft.

5. What will be the velocity of sound in air (both metric and English units) when the temperature is 22° ?

6. What is the temperature necessary to give the velocity of sound a value of 350 m.?

7. An experiment to determine the velocity of sound in air at 0° gave the following data: The report of a pistol was heard at a distance of 512 m. 1.5 seconds after firing. Average temperature 15°. Find velocity of sound at 0°. Assume that it is known what effect the temperature has on the velocity.

8. From the following data find what increase of velocity in air is caused by a rise of one degree in temperature: Sound travels 1714 m. in 5 sec. at 18°.

22. The law for velocity of sound in any medium is found by experiment to be: The velocity varies directly as the square root of the elasticity of the medium and inversely as the square root of its density, or

=

where V velocity, E a number representing relative elasticity, and D a number representing relative density.

9. If the velocity of sound in air is 332 m., what will it be in oxygen whose density is 1.105? Density of air 1.000. 10. If the velocity of sound in air of density .00129 is 332 m. per second, what will be the velocity in air whose density is .00258 ?

11. Air is about 14.5 times as dense as hydrogen. Find the velocity of sound in hydrogen ?

12. From the law given above show that the velocity of sound in air is not dependent upon barometric pressure. 13. If a mass of air were confined in a closed vessel of constant volume, would changes of temperature affect the velocity of sound in it? Illustrate your answer.

XLIII. WAVE-LENGTHS: VIBRATIONS.

1. The velocity of sound being 335 m. per second, what is the wave-length of a tone produced by 256 vibratione per second?

2. How many vibrations per second are required to produce a tone having a wave-length of 75 cm. when the velocity of sound is 33,000 cm. per second?

3. How many vibrations per second will produce soundwaves 5 ft. long, the temperature being 0° C. ?

4. A sound-wave may reach a point in a tube by two paths. When the two paths are 60 and 140 cm. long respectively the sound at the receiving point is at its minimum. Find (a) wave-length of the sound-waves, (b) the number of vibrations per second if the temperature at the time is 20° ?

5. A tuning-fork making 396 vibrations per second is sounded at one opening of a tube having two passages leading to a second opening. If the shorter passage is 60 cm. long, what must be the length of the other arm in order that no sound may be audible at the second opening?

6. A tuning-fork is held at the mouth of a tube whose diameter is 4 cm. When a movable diaphragm is so adjusted as to make the length of the tube 30 cm. the maximum resonant effect is observed. Find the number of vibrations of the fork per second?

NOTE.--Allowance for the effect of the diameter of the tube may be made by adding to the observed length of the tube one fourth of its diameter and using the result as the effective length.

7. What must be the length of a tube whose diameter is 6 cm. to respond most loudly to a tuning-fork of 320 vibrations per second?

8. A tuning-fork is held over a tall glass jar into which

water is gradually poured until the maximum reinforcement of the sound is produced. The length of the aircolumn is then found to be 52 cm. What is the vibrationnumber of the fork? The diameter of the tube may be disregarded.

9. A pendulum beating 150 times a minute (single vibrations) and a tuning-fork are arranged so as to record their movements on a smoked glass. It is found that the line made by the fork indicates 176 double vibrations between each two cross-marks of the pendulum. Find rate of vibration of the fork.

10. If the pendulum makes 90 single vibrations per minute, how many vibrations will be recorded between two pendulum-marks by a fork whose rate of vibration is 256 ?

23. Transverse Vibration of Strings.-The laws of vibration of strings may be summarized as follows:

The vibration-number, n, varies

(a) Inversely as the length, L.

(b) Directly as the square root of the tension, T.

(c) Inversely as the diameter, d.

(d) Inversely as the square root of the density, D.

XLIV. VIBRATION OF STRINGS.

1. Find the vibration-number of a string under stress of 40 kgm. if it is 256 under 50 kgm.

2. How long must a string be to have twice the rate of vibration of another similar string 1 m. long?

3. If a string whose length is 120 cm. vibrates 320 per second when under a tension of 60 kgm., what must be the tension of a wire of the same material and length, but whose diameter is two thirds that of the first, in order that have the same rate of vibration?

it may

4. Taking the density of iron as 7.8 and that of brass as