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?
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 into the equation I had before, y( t) = A cos(kt-w), be the way to go?