When I blow across the open mouth of the jar, or, better still, for the jar is too wide for this experiment, when I blow across the open end of a glass tube, t u, Fig. 95, of the same length as the jar, a fluttering of the air is thereby produced, an assemblage of pulses at the open mouth of the tube being generated. And what is the consequence? The tube selects that pulse of the flutter which is in synchronism with itself, and raises it to a musical sound. The sound, you perceive, is precisely that obtained when the proper tuning-fork is placed over the tube. The column of air within the tube has, in this case, virtually created its own tuning-fork; for by the reaction of its pulses upon the sheet of air issuing from the lips it has compelled that sheet to vibrate in synchronism with itself, and made it thus act the part of the tuning-fork.
Fig. 95.
Selecting for each of the other tuning-forks a resonant tube, in every case, on blowing across the open end of the tube, a tone is produced identical in pitch with that obtained through resonance.
When different tubes are compared, the rate of vibration is found to be inversely proportional to the length of the tube. These three tubes are 24, 12, and 6 inches long, respectively. I blow gently across the 24-inch tube, and bring out its fundamental note; similarly treated, the 12-inch tube yields the octave of the note of the 24-inch. In like manner the 6-inch tube yields the octave of the 12-inch. It is plain that this must be the case; for, the rate of vibration depending on the distance which the pulse has to travel to complete a vibration, if in one case this distance be twice what it is in another, the rate of vibration must be twice as slow. In general terms, the rate of vibration is inversely proportional to the length of the tube through which the pulse passes.
§ 13. Vibrations of Stopped Pipes: Modes of Division: Overtones
But that the current of air should be thus able to accommodate itself to the requirements of the tube, it must enjoy a certain amount of flexibility. A little reflection will show you that the power of the reflected pulse over the current must depend to some extent on the force of the current. A stronger current, like a more powerfully stretched string, requires a great force to deflect it, and when deflected vibrates more quickly. Accordingly, to obtain the fundamental note of this 24-inch tube, we must blow very gently across its open end; a rich, full, and forcible musical tone is then produced. With a little stronger blast the sound approaches a mere rustle; blowing stronger still, a tone is obtained of much higher pitch than the fundamental one. This is the first overtone of the tube, to produce which the column of air within it has divided itself into two vibrating parts, with a node between them. With a still stronger blast a still higher note is obtained. The tube is now divided into three vibrating parts, separated from each other by two nodes. Once more I blow with sudden strength; a higher note than any before obtained is the consequence.
In Fig. 96 are represented the divisions of the column of air corresponding to the first three notes of a tube stopped at one end. At a and b, which correspond to the fundamental note, the column is undivided; the bottom of the tube is the only node, and the pulse simply moves up and down from top to bottom, as denoted by the arrows. In c and d, which correspond to the first overtone of the tube, we have one nodal surface shown by dots at x, against which the pulses abut, and from which they are reflected as from a fixed surface. This nodal surface is situated at one-third of the length of the tube from its open end. In e and f, which correspond to the second overtone, we have two nodal surfaces, the upper one, x′, of which is at one-fifth of the length of the tube from its open end, the remaining four-fifths being divided into two equal parts by the second nodal surface. The arrows, as before, mark the directions of the pulses.
Fig. 96.