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## Homework Statement

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?

## Homework Equations

Equation for wave motion - is it this:

y(t ) = A cos (kt - w),

for some constants k,w.

## The Attempt at a Solution

v = sqrt (F/u) = sqrt (mg/ (m/L) ) = sqrt (gL)

this implies that velocity is constant for the wave. I was wondering if this was correct, since it looks suspicious.

From here, I'm not exactly sure where to go - which wave equation should I use to go further (to solve and find out what I want to find out?). Would plugging in to the equation I had before, y( t) = A cos(kt-w), be the way to go?