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 µ(x) increases uniformly from µ0 at x = 0 to µL at x = L.
(a) Find an expression for µ(x) as a function of x over the range 0 = x = L.
(b) Show that the time interval required for a transverse pulse to travel the length of the string is given by
