A string on a musical instrument is held under tension T

Chapter 16, Problem 66

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A string on a musical instrument is held under tension T and extends from the point x 5 0 to the point x 5 L. The string is overwound with wire in such a way that its mass per unit length m(x) increases uniformly from m0 at x 5 0 to mL at x 5 L. (a) Find an expression for m(x) as a function of x over the range 0 # x # L. (b) Find an expression for the time interval required for a transverse pulse to travel the length of the string.

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