EXAMINATION PAPERS. 289
A 80 _____
Therefore vib. No. at 80° F _ V x + 819 _ / 899 vib. .No. at 32° F 1 ~ V 819
2998 150 = 2862 = 113 verynearly-
That is, pitch will rise about 7 vibrations in 143, or about 1 in 20. More simply, 80° F is 80° — 32 = 48° above freezing point. Therefore if velocity of sound at 0° is 1090 above velocity at 48° F will be nearly 1090 + 48 = 1138.
vib. No. at 80° F 1138 114 Therefore ^ Nq ft(. 320 F _ im — 1Q9 nearly.
That is, a rise of about 5 in 109, or about 1 in 20 as before.
(e) Because strings whether of catgut or metal do not expand anything like so much as air for the same increase of temperature, but see p. 90.
2. Explain how it is that a sound can be reflected back from the open end of a tube. Explain the difference between this and the reflection taking place at a closed end of a tube.
Ant.—See pp. 60 and 61.
3. (a) What are Lissajous' figures ? (*) How are they produced i (c) What do they demonstrate ?
Am.—(a) Lissajous' figures are the figures described by a particle which is simultaneously vibrating in two directions, say at right angles to one another; or we may say, they are the figures obtained by optically combining the motions of two particles vibrating in directions at right angles to one another.
(b) There are various methods of producing them : one of the simplest is by means of such a compound pendulum as is figured in fig. 42. Fasten the lower end of this at one corner of the board with a piece of thread, load the funnel with sand and then release by burning the thread. The pendulum will then vibrate as a whole across the board in a direction parallel to a b—but the lower part will also vibrate in a direction at right angles to this parallel to A1 A, and the result will be a Lissajous' figure in sand on the board below, which remains at rest.
(e) They demonstrate the exact proportion or otherwise between the two vibration periods.
4. If mixed sand and lycopodium powder are scattered over a square brass plate clamped at its centre, and the plate is so bowed at its edge as to emit a shrill note, the sand is observed to settle down in lines, and the lycopodium in small patches. Explain the significance of these facts.