Chapter 16, Problem 58CP

Assume an object of mass M is suspended from the bottom of the rope of mass m and length L in Problem 48. (a) Show that the time interval for a transverse pulse to travel the length of the rope is

$\Delta t=2\sqrt{\frac{L}{mg}}(\sqrt{M+m}-\sqrt{M})$

(b) What If? Show that the expression in part (a) reduces to the result of Problem 48 when M = 0. (c) Show that for m << M, the expression in part (a) reduces to

$\Delta t=\sqrt{\frac{mL}{Mg}}$