velocity as a condensation. We
must therefore remember, that just behind the wave of condensation is
the wave of rarefaction, both travelling with the same velocity, and
therefore always maintaining the same relative position to each other.
Now, the fork vibrates a great many times in a second, and will
consequently generate as many of these waves, all of them constituted
alike, and having the same length; by length meaning the sum of the
thicknesses of the condensation and the rarefaction. Suppose a fork to
make one hundred vibrations per second: at the end of the second, the
wave generated by the vibration at the beginning of the second would
have travelled, say, eleven hundred feet; and evenly distributed between
the fork and the outer limit, would be ranged the intermediate waves
occupying the whole distance: that is to say, in eleven hundred feet
there would be one hundred sound-waves, each of them evidently being
eleven feet long. If the fork made eleven hundred vibrations per second,
each of these waves would be one foot long; for sound-waves of all
lengths travel in air with the same rapidity. Some late experiments seem
to show that the actual amplitude of motion of the air, when moved by
such a high sound as that from a small whistle, is less than the
millionth of an inch.

PITCH.

The pitch of a sound depends wholly upon the number of vibrations per
second that produce it; and if one of two sounds consists of twice as
many vibrations per second as the other one, they differ in pitch by the
interval called in music an octave, this latter term merely signifying
the number of intervals into which the larger interval is divided for
the ordinary musical scale. The difference between a high and a low
sound is simply in the number of vibrations of the air reaching the ear
in a given time. The smaller intervals into which the octave is divided
stand in mathematical relations to each other when they are properly
produced, and are represented by the following fractions:--

C D E F G A B C
1 9/8 5/4 4/3 3/2 5/3 15/8 2

[Illustration]

These numbers are to be interpreted thus: Suppose that we have a
tuning-fork giving 256 vibrations per second: the sound will be that of
the standard or concert pitch for the C on the added line as shown on
the staff. Now, D when properly tuned will make 9 vibrations while C
makes but 8; but, as C in this case makes 256, D must