A pipe open at both ends is capable of emitting a note. But we shall find, if we experiment, that the note of a stopped pipe is an octave lower than that of an open pipe of equal length. This is explained by Fig. 137, 1. The air-column in the pipe (of the same length as that in Fig. 136) divides itself, when an end is blown across, into two equal portions at the node B, the natural point to obtain equilibrium. A pulse will pass from A or A1 to B and back again in half the time required to pass from A to B and back in Fig. 136, 1; therefore the note is an octave higher.
Fig. 137.—Showing how harmonics of an open pipe are formed, B, B1, and C are "nodes." The arrows indicate the distance travelled by a sound impulse from a node to a node.
THE OVERTONES OF AN OPEN PIPE.
The first overtone results when nodes form as in Fig. 137, 2, at points one-quarter of the length of the pipe from the ends, giving one complete ventral segment and two semi-ventral segments. The vibrations now are twice as rapid as before. The second overtone requires three nodes, as in Fig. 137, 3. The rate has now trebled. So that, while the overtones of a closed pipe rise in the ratio 1, 3, 5, 7, etc., those of an open pipe rise in the proportion 1, 2, 3, 4, etc.
WHERE OVERTONES ARE USED.
In the flute, piccolo, and clarionet, as well as in the horn class of instrument, the overtones are as important as the fundamental notes. By artificially altering the length of the column of air, the fundamental notes are also altered, while the harmonics of each fundamental are produced at will by varying the blowing pressure; so that a continuous chromatic, or semitonal, scale is possible throughout the compass of the instrument.
THE ORGAN.
From the theory of acoustics[30] we pass to the practical application, and concentrate our attention upon the grandest of all wind instruments, the pipe organ. This mechanism has a separate pipe for every note, properly proportioned. A section of an ordinary wooden pipe is given in Fig. 138. Wind rushes up through the foot of the pipe into a little chamber, closed by a block of wood or a plate except for a narrow slit, which directs it against the sharp lip A, and causes a fluttering, the proper pulse of which is converted by the air-column above into a musical sound.
