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Any

the density of any gas is also directly proportional to the pressure. increase of pressure increases both E and D in the same proportion, and hence their ratio remains constant. Thus the velocity is independent

of the pressure.

E

31. Effect of Temperature.-It is otherwise when the temperature of the air changes. For suppose that the temperature rises and consider how this will affect the quantities in equations (1) or (3). Since the air is free to expand, the pressure or elasticity will remain unaltered. But the density of the air diminishes just as its volume increases (the density of a given mass of gas being inversely proportional to its volume). Thus rise of temperature produces an increase in the velocity, as stated in Art. 19.

If the temperature rises from o° to to, the volume increases in the ratio of 1 to (1+at), and the density diminishes in the ratio of (1+ at) to I. From this it may easily be seen that if V, denote the velocity of sound in air at o°, its velocity at any temperature will be

V1 =Vo√i+at.

32. Velocity in other Gases.-The equations for the velocity given in Arts. 28 and 29 hold good not only for air but also for other gases. It therefore follows that the velocity in any gas is inversely proportional to the square root of the density of the gas.

For example, oxygen is sixteen times as dense as hydrogen. Hence the velocity of sound in oxygen is to that in hydrogen as √ √16, or

as 1 : 4.

CHAPTER IV

REFLECTION OF SOUND

33. Reflection of Longitudinal Waves.-A good idea of the way in which sound-waves are reflected may be obtained by studying the reflection of longitudinal waves at the end of a wire spiral such as was used in Expt. 5. The reflection takes place in two distinct ways, according as the end is free or fixed. In both cases we shall suppose the original (or incident) pulse to be a pulse of compression.

EXPT. 10. Reflection from a Free End.-The spiral is supposed to be in the state shown in Fig. 6 (both ends free). A pulse of compression is sent from one end-say the righthand when it reaches the other end, it does not disappear but is reflected as a pulse of rarefaction. When it returns to the right-hand end it is again reflected, but now as a pulse of compression again. Thus at each reflection at a free end the wave suffers a change of type: a pulse of rarefaction being reflected as a pulse of compression and vice versâ.

EXPT. II. Reflection at a Fixed End.-Push one end of the spiral into a cork and clamp this fast to a heavy retortstand. Send a pulse of compression along the spiral from the free end. When the pulse reaches the fixed end the motion of the coils is reversed and the wave is reflected back, but still as a pulse of compression. In the same way a pulse of rarefaction is reflected as a pulse of rarefaction. In reflection from a fixed end there is no change of type. The cases of reflection to which we shall for the present restrict our attention are of

the same kind as those which occur at the fixed end of a spiral.

34. Reflection of Sound-Waves. Sound-waves are reflected from solid obstacles in much the same way as the longitudinal waves in the last experiment. Each pulse of compression or rarefaction, when it reaches the obstacle, is reflected, giving rise to a pulse of compression or rarefaction travelling in the opposite direction.

In the case of light we saw that in order to get good reflection it was necessary that the reflecting surface should be smooth and polished: in the case of sound the most essential thing is that the reflecting surface should be of considerable extent. You will doubtless recollect instances in which you have heard band-music or the sound of church-bells apparently reaching you in a direction totally different from that of the band or steeple, the sound being reflected from a wall or row of houses.

35. Echoes.-An echo is produced when a sound is reflected normally (or back along its own path) from a high cliff or wall. If a person standing at a sufficient distance from the cliff shouts or claps his hands, he hears the sound repeated. In order that he may hear the echo distinctly it is necessary that the time taken by the sound in travelling to the cliff and back again should be sufficiently long to enable him to distinguish between the original and the reflected sound, for otherwise the two would be confused together.

Suppose that we allow one-fifth of a second for this; and further that we take the velocity of sound as 1100 ft. per second. In one-fifth of a second sound travels 220 ft., so that we must allow for I10 ft. to the cliff and 110 back to the observer. Thus in order to hear the echo distinctly the observer's distance from the cliff should not be much less than IIO ft.

36. Sensitive Flames.-In experimenting on reflection of sound (and especially for class demonstration) it is convenient to have some means of indicating the presence and whereabouts of a sound. This is best done by means of sensitive flames.

When the pressure of the gas supplied to a jet is gradually increased, a point is reached at which the flame begins to flare just at this point it becomes very sensitive to sound and especially to hissing and tinkling sounds. The flame should be long, thin, and straight, as shown in the accompanying figure. A suitable jet can be made by drawing out a piece of glass tubing to about 2 mm. diameter, cutting it off with a file and grinding the edge smooth on a stone. But as glass jets are very liable to crack, it is better to get a plain steatite burner with a small round hole. The sensitiveness of a flame depends upon the burner and upon a proper regulation of the gas-pressure: sometimes a burner is so sensitive that it is scarcely possible to work with it. The flame can be protected from accidental noises by surrounding it with a glass globe

A

Fig. 13.

B

provided with suitable openings; into one of these may be inserted a funnel for the purpose of catching the sound and directing it towards the base of the flame.

EXPT. 12.-Procure a gas-bag (a rubber bag such as is used for lantern work), press it down flat to squeeze out all air, and then connect it by rubber tubing to the gas-supply. Raise the pressureboards, so as to let the gas stream in freely, and when the bag is full of coal-gas close the tap attached to the bag. Connect the tubing to the sensitive jet. Put on the pressure-boards and place weights on them so as to increase the pressure until the jet begins to flare. Now reduce the pressure slightly and you will find that the flame is in the sensitive state. It has the form shown in A, Fig. 13. The slightest noise makes the flame

roar, and at the same time it becomes shorter and broader

and jagged at the edges, as shown in B.

Stand a few feet from the flame and shout: each time it ducks down. Try singing and whistling. Talk to it and see how it picks out the s sounds. Rattle a bunch of keys: it roars furiously.

37. Experiments on Reflection of Sound. The reflection of sound may be illustrated in the same way and with the same apparatus as that described on pp. 99-101 for demonstrating the reflection of heat-radiation.

EXPT. 13.—Arrange the tin tubes and reflector as shown in Fig. 59, p. 100. For the present purpose the tubes may be somewhat longer than those used for the radiation experiment say 4 ft. long each. At T place the sensitive flame, adjusting the mouth of the funnel over the end of the tube. It may be necessary to screen the flame from sound travelling directly from B to it: this can be done by hanging wet towels across between B and T to act as sound-screens. Or the sound may be prevented from getting outside as follows: Make a loose sleeve of cloth and tie it over the end of the tube at B. Take a small piece of tinp-late in one hand and a penny in the other. Place both hands well inside the sleeve and tap the penny against the tin-plate. If the reflector at R is properly adjusted, the flame will now respond, ducking down at each tap. Remove the reflector R. If the flame is still affected, try tapping more gently.

EXPT. 14. Repeat the experiment by hanging a watch in front of the tube at B and using your ear in place of the sensitive flame at T. The ticking is much more distinctly heard when the reflector is in position than when it is removed.

EXPT. 15. Place the two tubes end to end and in a straight line so as to form one tube 8 ft. long. At this distance the ticking of a watch is not audible in free air. But if you hang a watch in front of one end of the tube and apply your ear to the other end, you will hear the ticking with surprising distinctness.

This will enable you to understand how 'speaking-tubes' can be used for communicating between different rooms in a building. Their behaviour may be explained as a result of

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