FLUE-PIPES AND SEEDS. |
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ing very gently into the pipe, so as to produce its fundamental, all three flames are agitated, but the central one most so. Turning down the gas till the flames are very small, and blowing again, the middle one will be extinguished, while the others remain alight.
Inasmuch as the two ends of an open pipe must, as we have shown, correspond to the middle of ventral segments, the next simplest way in which such a pipe can vibrate, is, with two nodes, as shown in fig. 54 B. In A there are two half segments, which are equivalent to one; in B there are two half segments and one whole one, equivalent to two segments; the rate of vibration in B will therefore be twice as rapid as in A. Accordingly, we find that the next highest tone to the fundamental, which can be produced from an open pipe, is its octave. The occurrence of the two nodes in B can be experimentally proved by the pipe of fig. 55, for if this pipe be blown more sharply, so as to produce the octave of the fundamental, the two flames A and C will be extinguished, while B will remain alight. C and D, fig. 54, represent the next simplest forms of vibration with three and four nodes respectively. The rate of vibration in (C) and (D) will obviously be three and four times respectively that in (A). Proceeding in this way, it will be found that the rates of all the possible modes of segmental vibration in an open pipe, will be as 1, 2, 3, 4, 5, &c, and this result, thus theoretically arrived at, is confirmed by practice; for we have seen that, calling the fundamental tone (d|); the harmonics produced from such a pipe are, the vibration numbers of
which are as 2, 3, 4, 5, &c.
We have hitherto supposed that each of these notes successively appears alone, but this is rarely the case, usually the fundamental is accompanied by one or more of these tones. When they are thus simultaneously produced, it is convenient to term them overtones, or, together with the fundamental, partials, as in the case of stretched strings. In order to explain the simultaneous production of these partials, we simply have to suppose the simultaneous occurrence of the segmental forms represented in fig. 5 i. We thus see that the notes obtainable simultaneously from an open pipe, are the
complete series of partial tones, whose rates of vibration are as the numbers 1, 2, 3, 4, 5, &c.Coming now to stopped pipes we have seen in Chap. VII, page 61, that a pulse of condensation entering a stopped pipe, travels to the closed end, and is there reflected back unchanged. On arriving at the open end, it is reflected back as a pulse of rarefaction, which on |
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