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Wave through uniform rope

  • Thread starter wayfarer
  • Start date
  • #1
9
0

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?
 

Answers and Replies

  • #2
44
0
F is not a constant in this case, each part of the rope is beeing stretched differently depending on how close it is to the ceiling
 
  • #3
9
0
In that case, how would I deal with a situation where F is not constant? I have only learnt so far how to deal with cases where it is constant.
 
  • #4
44
0
the equation for v is still valid you just have to write F in terms of x (where x is distance from the bottom part of the rope)
 
  • #5
Doc Al
Mentor
44,871
1,119
You'll need to integrate. Find the speed of the wave as a function of position along the rope. (What's the tension as a function of position?)
 

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