proportional to the
length of the pipe. Thus, the vibrations of a two-foot pipe are twice as
rapid as those of a four-foot pipe, and the note emitted by the former
is an octave higher than that of the latter. A one-foot pipe gives a
note an octave higher still. We are here speaking of the _fundamental_
tones of the pipes. With them, as in the case of strings, are associated
the _overtones_, or harmonics, which can be brought into prominence by
increasing the pressure of the blast at the top of the pipe. Blow very
hard on your key, and the note suddenly changes to one much shriller. It
is the twelfth of the fundamental, of which it has completely got the
upper hand.

We must now put on our thinking-caps and try to understand how this
comes about. First, let us note that the vibration of a body (in this
case a column of air) means a motion from a point of rest to a point of
rest, or from node to node. In the air-column in Fig. 136, _1_, there is
only one point of rest for an impulse--namely, at the bottom of the
pipe. So that to pass from node to node the impulse must pass up the
pipe and down again. The distance from node to node in a vibrating body
is called a _ventral segment_. Remember this term. Therefore the pipe
represents a semi-ventral segment when the fundamental note is sounding.

When the first overtone is sounded the column divides itself into two
vibrating parts. Where will the node between them be? We might naturally
say, "Half-way up." But this cannot be so; for if the node were so
situated, an impulse going down the pipe would only have to travel to
the bottom to find another node, while an impulse going up would have
to travel to the top and back again--that is, go twice as far. So the
node forms itself _one-third_ of the distance down the pipe. From B to A
(Fig. 136, _2_) and back is now equal to from B to C. When the second
overtone is blown (Fig. 136, _3_) a third node forms. The pipe is now
divided into _five_ semi-ventral segments. And with each succeeding
overtone another node and ventral segment are added.

The law of vibration of a column of air is that the number of vibrations
is directly proportional to the number of semi-ventral segments into
which the column of air inside the pipe is divided.[29] If the
fundamental tone gives 100 vibrations per second, the first overtone in
a closed pipe must give 300, and the second 500 vibrations.

THE OPEN PIPE.

A pipe open at both ends is capable