Science and music / [by Sir James Jeans].

  • Jeans, James, 1877-1946.
Date:
1947
Catalogue details

Licence: In copyright

Credit: Science and music / [by Sir James Jeans]. Source: Wellcome Collection.

    101/300 (page 79)
    original curve repeats itself regularly at intervals of one foot, we need only employ curves which repeat them¬ selves regularly i, 2, 3, 4, etc. times every foot—i.e. waves of lengths 12, 6, 4, 3, etc. inches. This is almost obvious, for waves of other lengths, such as 18 or 5 inches, would prevent the composite curve repeating regularly every foot. If the original curve does not repeat regularly, we treat its whole length as the first half-period* of a curve which does repeat, and obtain the theorem in its more usual form. It tells us that the original curve can be built up out of simple harmonic constituents such that the first has one complete half-wave within the range of the original curve, the second has two complete half¬ waves, the third has three, and so on; constituents which contain fractional parts of half-waves need not be employed at all. There is a fairly simple rule for calculating the amplitudes of the various constituents, but this lies beyond the scope of the present book. We obtain a first glimpse into the way of using this theorem if we suppose our original curve to be the curve assumed by a stretched string at any instant of its vibration. Figs. 24, 25 and 26 on p. 67 shew groups of simple har¬ monic curves which contain one, two and three complete half-waves respectively within the range of the string. Let us imagine this series of diagrams extended indefinitely so as to exhibit further simple harmonic curves containing 4, 5, 6, 7 and all other numbers of complete half-waves. Then the series of curves obtained in this way is precisely the * It might seem simpler to treat the original curve as a whole period of a repeating curve, but there are mathematical reasons against this.