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 over wound with wire in such a way that its mass per unit length μ(x) increases uniformly from + 0 at x = 0 to μL at x = L.
(a) Find an expression for μ(x) as a function of x over the range 0 2 x 2 L.
(b) Show that the time interval required for a transverse pulse to travel the length of the string is given by