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288                    HAND-BOOK OF ACOUSTICS.
Afternoon. 2 to 5.
1.    What explanation can you offer of the following ?
(a)  The throbbing sound so often heard when the tone of a large bell is dying away.
(b)  The circumstance that the upper partial tones of church bells do not even approximately follow the harmonic series 1:2:3:4 &c.
Am.—{a) and (b) See pp. 125 and 126.
2.   (a) Briefly state Helmholtz's Theory of Consonance. (4) It in
found that if two notes jwj               are played simultaneously upon
an open and a stopped pipe, the interval sounds harsher, if the lower note is taken by a stopped pipe while the upper note is played upon an open pipe, than is the case if the upper is played upon a stopped pipe and the lower upon an open pipe. Explain this.
Am.—(a) See Chapter XV.
(b) See p. 198 with fig. 82, last interval.
3.    Sketch the wave forms for a note, for its octave, and for th<i note that is a fifth above its octave, assuming that each is of equal loudness ; also show how to find the complex wave form of the sound produced by all these three notes sounding together as a chord.
Am.—See pp. 82 with fig. 45.
4.    What is the effect on the apparent pitch of a note under the following various circumstances :—(a) when the instrument which sounds the note is moving rapidly (as when the performer is carried on board a railway train) towards the observer; (b) when a wind is blowing towards the observer from the place where the instrument is situated; (c) when the observer is moving rapidly (say, on board a train) towardn the place where the instrument is situated.
Am.—(a) The note is apparently sharpened in all three cases.
Tuesday, December 13th, 1899. Morning, 10 to 1.
1. (a) What change does a rise of temperature produce upon the velocity of sound in air? (b) Suppose an organ-pipe to be in tune when blown with air at the freezing point, how much will its pitch rise when blown with air at 80°F ? (e) Why do not stringed instruments change in pitch to the same extent.
Am.—(a) It increases the velocity : See p. 20 and p. 100.
/             \ 5                      5 80
(J) 80°F = (80 — 32J g C° as 48 X y = -3 ss: 26|°C
Therefore if v denotes velocity of sound at 0°C
v V 1 + y x 273 "wiU be the velocity at 80°F (see p. 100).