Barton, Edwin H. (Edwin Henry), b. 1858 · London, Macmillan and Co., limited · leaf 445
these experimental results as a basis, 424 SOUND CHAP. VIII Helmholtz has given an analysis of the motion of a bowedstring which, with slightly different notation, is followedhere. 348. Theory of Bowed Strings by Helmholtz.—Letthe motion of a point on the string be as represented inFig. 87, and be… … Fig. 87.—Motion of Well-bowed String. Now let y be developed in the Fourier series, y = ax cos cot + a2 cos 2cot + . . . + an cos ncot + .+ &i sin cot + b2 sin 2cot +. . . + bn sin ncot + . . . where cor = 27r, and the values of the coefficients are to beobtained from the theorem by integration…
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