ars a
note two octaves above the "fundamental note" of which the string is
capable.

It is entirely possible, however, for a string to vibrate simultaneously
in a number of ways and so to give not only its fundamental note but
several others at the same time. The photographs[8] of Fig. 80 of Pl.
VII illustrate this possibility.

What happens then to the molecules of air which are adjacent to the
vibrating string? They must perform quite complex vibrations for they
are called upon to move back and forth just as if there were several
strings all trying to push them with different frequencies of vibration.
Look again at the pictures, of Fig. 80 and see that each might just as
well be the picture of several strings placed close together, each
vibrating in a different way. Each of the strings has a different
frequency of vibration and a different maximum amplitude, that is,
greatest size of swing away from its straight position.

[Illustration: Fig 81]

Suppose instead of a single string acting upon the adjacent molecules we
had three strings. Suppose the first would make a nearby molecule move
as in Fig. 81A, the second as in Fig. 81B, and the third as in Fig. 81C.
It is quite evident that the molecule can satisfy all three if it will
vibrate as in Fig. 81D.

Now take it the other way around. Suppose we had a picture of the motion
of a molecule and that it was not simple like those shown in Fig. 78 but
was complex like that of Fig. 81D. We could say that this complex motion
was made up of three parts, that is, had three component simple motions,
each represented by one of the three other graphs of Fig. 81. That means
we can resolve any complex vibratory motion into component motions which
are simple.

It means more than that. It means that the vibrating string which makes
the neighboring molecules of air behave as shown in Fig. 81D is really
acting like three strings and is producing simultaneously three pure
musical notes.

Now suppose we had two different strings, say a piano string in the
piano and a violin string on its proper mounting. Suppose we played both
instruments and some musician told us they were in tune. What would he
mean? He would mean that both strings vibrated with the same fundamental
frequency.

They differ, however, in the other notes which they produce at the same
time that they produce their fundamental notes. That is, they differ in
the frequencies and amplitudes of these other component