A uniform rope of length L and negligible stiffness hangs from a solid fixture in the ceiling. The free lower end of the rope is struck sharply at time t=0. What is the time t it takes the resulting wave on the rope to travel to the ceiling, be reflected, and return to the lower end of the rope?

Question

Physics

Jakobe Leonard

19 February, 15:39

A uniform rope of length L and negligible stiffness hangs from a solid fixture in the ceiling. The free lower end of the rope is struck sharply at time t=0. What is the time t it takes the resulting wave on the rope to travel to the ceiling, be reflected, and return to the lower end of the rope?

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Ally Roberts · Answer 1

The wave produced is a standing wave.

y' = [2ymax - kx] cos wt.

y max is maximum displacement, k is angular wave number, x is equal to the length L, w is angular frequency, t is time.

The time taken for the wave to travel to the ceiling and get reflected is given as:

t = 1/f = (2L) / nv. Where n =, 1,2,3, ... and v is wave speed, f is wave frequency.