Serway & Jewett — Wave Motion: Problem 57

A string on a musical instrument is held under tension \( T \) and extends from the point \( x = 0 \) to the point \( x = L \). The string is overwound with wire in such a way that its mass per unit length \( \mu(x) \) increases uniformly from \( \mu_0 \) at \( x = 0 \) to \( \mu_L \) at \( x = L \). (a) Find an expression for \( \mu(x) \) as a function of \( x \) over the range \( 0 \le x \le L \). (b) Find an expression for the time interval required for a transverse pulse to travel the length of the string.