Handbook of Acoustics for the Use of Musical Students

Handbook of Acoustics for the Use of Musical Students

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This historic book may have numerous typos and missing text. Purchasers can download a free scanned copy of the original book (without typos) from the publisher. Not indexed. Not illustrated. 1897* edition. Excerpt: ... Summation tones. This theory is difficult to explain, without such recourse to mathematics, as would be unsuitable to a work like this. We must be content, therefore, to state it in general terms as follows: When two series of sound-waves simultaneously traverse the same mass of air, it is generally assumed that the resultant motion of the air particles is equal to the algebraic sum of the motions, that the air particles would have had, if the two series had traversed the mass of air, independently of one another. This, however, is only strictly true, when the amplitudes of the soundwaves are very small, that is, when the air particles oscillate only through very small spaces. When the amplitudes of the waves are at all considerable in proportion to their length, secondary-waves are set up, which on reaching the ear give rise to Combination Tones. The higher octave of the fundamental tone, which may be frequently heard, when a tuning-fork is sharply struck, has a similar origin. Summation Tones. Helmholtz, as already mentioned, worked out the theory just referred to, mathematically, and proved that two tones with given vibration numbers, may not only produce a third tone, having its vibration number equal to their difference, but also another tone equal to their sum. To this latter sound, the term "Summation Tone" is applied. It is not difficult to satisfy oneself experimentally of the reality of the summation tones on such an instrument as the Harmonium or American Organ; indeed, these tones are much louder than is generally supposed. Thus if F2 and C be selected, the summation tone will be A, which with careful attention may generally be detected; the following table gives in the last column the summation tones that may be produced...show more

Product details

  • Paperback | 80 pages
  • 189 x 246 x 4mm | 159g
  • Rarebooksclub.com
  • Miami Fl, United States
  • English
  • Illustrations, black and white
  • 1236639774
  • 9781236639776