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Transverse Wave Properties

A uniform rope of mass m and length L hangs from a ceiling.
(a) Show that the speed of a transverse wave in the rope is a function of y, the distance from the
lower end, and is given by v = Sqrt(gy).
(b) Show that the time it takes a transverse wave to travel the length of the rope is given by t =
2sqrt(L/g). (Hint: calculate the length of time to travel a length dy at distance y on the rope first).
(c) Does the actual mass of the rope affect the results of (a) and (b)?

Solution Summary

This solution contains an annotated diagram and step-by-step calculations with explanations to determine the speed of the transverse wave and the time it takes to travel the length of the rope.