Acoustics, Theoretical Volume 1

Acoustics, Theoretical Volume 1

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This historic book may have numerous typos and missing text. Purchasers can usually download a free scanned copy of the original book (without typos) from the publisher. Not indexed. Not illustrated. 1870 edition. Excerpt: ...simple, and may be left to the reader. 129. We have so far supposed, for simplicity, that the obligatory motion was a simple harmonic vibration. But if it were a compound vibration consisting of the superposition of any number of harmonic vibrations of different periods, phases, and amplitudes, it would be easily shewn that every one of these components would produce a corresponding term (analogous to (7)) in the expression for the forced vibrations of the string. Thus, if the imposed vibration required that, when x = b, the forced vibration of the string, from x = o to x = b, would be expressed by the equation In this case, if Ti---, that is, if the period of every com1 a ponent of the imposed vibration is some aliquot part of the natural period of the whole string, then the above expression is not altered by changing x and b into l--x and l--b; and therefore it holds good for the whole string. 130. These results may be approximately verified by experiment as follows: If a tuning-fork be struck, and the end of its stalk be then placed on the string of a pianoforte, violin, or violoncello, at any point, it may be considered approximately as imposing an obligatory vibration on that point. And it will be found that in general the only sound heard is the note of the tuning-fork, very weak. If, however, the point of application be such that the portion of string intercepted between it and either end could vibrate naturally so as to give, either as a fundamental tone or as a harmonic, one of the component tones of the tuning-fork, then that portion of the string is thrown into strong vibration, so as to give the corresponding tone very distinctly. The fundamental tone of a tuning-fork is by far the strongest of its component tones. The more

Product details

  • Paperback | 66 pages
  • 189 x 246 x 4mm | 136g
  • United States
  • English
  • black & white illustrations
  • 1236746562
  • 9781236746566