Let’s consider a string on a piano that is held under tension T and extends from the point x = 0 to the point x = L. The mass per unit length of the string (x) increases linearly from 0 at x = 0 to L at x = L. (a) Find an expression for (x) as a function of x. (b) Show that for a transverse pulse, the time interval needed to travel the whole length of the string is given by