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5. Give a brief summary of the various theories which have been put forward to explain a consonance and a dissonance. Am.—See p. 172.
Afternoon. 2 to 5.
1.  (a) Using a graphic representation of sound-waves in air, point out what, in your representation, determine respectively the pitch, loudness, and the quality of the sound ?
(£) State very briefly the evidence for your statement.
Am. (a) See pp. 19 and 22.
(b) Pitch varies with vibration rate. Proved by Syren, &c.
Wave-length=Velocity divided by vibration rate (see p. 39);
Therefore pitch depends upon length of sound-wave.
Loudness depends upon amplitude. See p. 52.
Quality depends upon form. See p. 80.
2.    If you stand near equally spaced palisading, with vertical stakes a few inches apart, and sharply clap your hands, there is an echo with a musical tone. Explain this, and show how the tone may be determined from the velocity of sound and the distance between the stakes.
Am.—The sound will be reflected back by each of the stakes. Suppose, for simplicity, you are close to one of the stakes and that the clap caused one sound-wave only ; part of this sound-wave striking the next stake is reflected back to your ear; another part travels to next stake, is reflected and reaches your ear in its turn, and so on. The length of this sound-wave therefore is twice the distance between the stakes, and thus the vibration number of the tone produced is found by dividing the velocity of sound by twice this distance.
3.   (a) How may the velocity of sound in a pipe, closed at one end by a movable piston, be determined by resonance to a fork of known frequency P
(b)  Give the theory of the experiment, and a general explanation of the need for the end correction ?
(c)  How may the experiment be conducted so as to eliminate the end correction ?
Am. (a) See p. 119.
(b)  See p. 61 and 62.
The reflection from the open end does not take place exactly at the end, but at a distance from it of about £ of the radius of the tube; this is called the end correction.
(c)  Ascertain the position of the upper node in B fig. 56 (see p. 103). Measure distance of this node from closed end and multiply this by | X 4to obtain the wave-length.