Upon p. 63 is given a picture of the form of a simple sound-wave in air,
which, as described, consists of two parts, a condensation and a
rarefaction. All simple sound-waves have such a form; but when two or
more sound-waves that stand in some simple ratio to each other, as do
the sounds of musical instruments, are formed in air, the resulting wave
is more or less complex in structure; and where there are many
components, as there are where a number of different kinds of
instruments are all sounding at once, it is well-nigh impossible to
figure even approximately the form of such wave-combinations. It is
generally given in treatises upon sound with ordinates representing the
factors with their relative intensities. When the extremities of the
ordinates are connected, there is drawn a curved line with regularly
recurring loops. This cannot give a correct idea of the form of the
wave, because the motion of a particle of air is not up and down like a
floating body upon waving water, but it is forward and back, in the
direction of the motion of the wave.
In Fig. 10 three simple sound-waves are thus represented at 1, 2, and 3,
these having the wave-length 1, 2, and 3. In 4, the three are combined
into one compound wave, and better show the form of a transverse section
of such a sound-wave in the air. The organ-pipe called the principal
gives out such a compound wave as is seen by referring to the table on
p. 91. The second overtone, however, is quite weak in that pipe, which
would so modify the form as to lessen somewhat the density at _b_, and
increase it at _a_.
[Illustration: FIG. 10.]
In like manner the space in the length of the fundamental sound,
whatever it may be, is divided up into a number of minor condensations
and rarefactions, which may strengthen each other, or so interfere as to
change the position of both; as is seen in the figure at _b_, where the
condensation due to wave 2 interferes with the rarefaction of 3.