Sound / by John Tyndall.

  • Tyndall, John, 1820-1893.
Date:
1893
Catalogue details

Licence: Public Domain Mark

Credit: Sound / by John Tyndall. Source: Wellcome Collection.

    208/496 (page 180)
    augment in the proportion of the series of odd numbers, 1 ! 3 : 5. And could we obtain still higher notes, their relative rates of vibration would continue to be represented by the odd numbers, 7, 9, 11, 13, &c. &c. It is evident that this must be the law of succession. For the time of vibration in c or d is that of a stopped tube of the length xy; but this length is one-third of the length of the whole tube, consequently its vibrations must be three times as rapid. The time of vibration in e or/ is that of a stopped tube of the length x' y\ and inasmuch as this length is one-fifth that of the whole tube, its vibra- tions must be five times as rapid. We thus obtain the succession 1, 3, 5, and if we pushed matters further we should obtain the continuation of the series of odd numbers. It is now once more in your power to subject my statements to an experimental test. Here are two tubes, one of which is three times the length of the other. I sound the fundamental note of the longest tube, and then the next note above the fundamental. The vi- brations of these two notes are stated to be in the ratio of 1 13. This latter note, therefore, ought to be of precisely the same pitch as the fundamental note of the shorter of the two tubes. When both tubes are sounded their notes are identical. It is oidy necessary to place a series of such tubes of different lengths thus together to form that ancient instru- o o ment, Pan’s pipes, P p', fig. 97, with which we are so well acquainted. The successive divisions, and the relation of the over- tones of a rod fixed at one end (described in p. 163b, are