HANDBOOK OF ACOUSTICS - online book

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302                    HAND-BOOK OF ACOUSTICS.
Am.—The difference between a diatonic semitone and the greater
16 135 16 128 2048 chromatic semitone = v> + m = 15 * m = -Ml,
it is called the Diaskhisma. The difference between a diatonic semitone
. x. ,          ,.                 .x            16 25 16 24 128
and the lesser chromatic semitone = TK-r22 = r~Xo5 = foe
It is called the Enharmonic or Great Diesis.
5.    Supposing this note ^Trr           to give 520 vibrations per second
find the vibration numbers of the minor 7th above it, produced (1) by
a perfect 5th added to a minor 3rd, and (2) by the sum of two perfect
4ths.
520          3          6
Ant.— -j- X g X 5 = 936
520          4          4
-j X 3 X 3 = 924-4
/E
6.    How is the formula v y: modified so as to apply to the
velocity of sound in air ?
In the case of air E represents the elasticity of air, which is measured by the ratio of the pressure applied to the compression produced. Thus, if a certain volume of air under a pressure P is submitted to a small additional pressure p, then, by Boyle's law, the diminution in
P                                                             P
volume thus caused will be p; consequently E is the ratio of p to j,
that is—
This, however, is only true if the compression produces no rise iu temperature ; but heat is always produced during compression. And in the case of sound waves the compression is so rapid that the heat has not time to escape, and thus a rise of temperature occurs during the condensation. The amount of heat produced is proportional to the compression, and this increases the elasticity of the air in the same proportion. The amount by which the elasticity of the air is thus increased has been found by experiment to be 141, so that the formula—
V = yj becomes V = y/**£* Expressing P and D in our English units : Z>, the density or weight of