Serway & Jewett — Wave Motion: Problem 58

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 \(\Delta t = 2 \sqrt{\frac{L}{mg}} \left( \sqrt{M + m} - \sqrt{M} \right)\). (b) What If? Show that the expression in part (a) reduces to the result of Problem 48 when \(M = 0\). (c) Show that for \(m \ll M\), the expression in part (a) reduces to \(\Delta t = \sqrt{\frac{mL}{Mg}}\).