# Power of a transverse wave related to rope length

1. Jul 16, 2011

### symphwar

1. The problem statement, all variables and given/known data
Two traveling transverse waves propagate
down two long ropes under the conditions
that the linear mass density, tension, and
transverse displacement amplitude for the two
ropes are the same, but that one rope has
twice the length of the other.
If the shorter rope has a power P0 being
transmitted along its length, then what is the
power, P, being transmitted down the longer
rope?
1. P = 1/4 P0
2. P = 4 P0
3. P = 1/2 P0
4. P = 2 P0
5. P = P0

2. Relevant equations
P = 1/2 uvA2w2
(u = linear mass density, w = angular frequency, v = phase speed)
v = sqrt(T/u)
(T = tension)

v = w/k
(k = wavenumber = 2pi/wavelength)

3. The attempt at a solution
Given that phase speed is related to tension and linear mass density, I think the values of u, A, and v are the same for both ropes. The only variable remaining is w, and I can't seem to infer what its value might be with the stated information.
Trying to find a relation with w and the given information, I realize I also do not know k or wavelength.
My understanding of a wave's power is that, with a given medium, w is controlled by the person/oscillator generating the wave. Could it be that it is implied w is the same for both waves, so that P = P0?

2. Jul 16, 2011

### BruceW

I think you have the correct answer. The wave travelling down the rope could have any arbitrary value for w, (which would depend on how quickly the person/oscillator moved the rope up and down). So maybe you were supposed to assume the same oscillator was used for both ropes, so w is the same for both, so the power is the same.

In any case, you are right that the power transmitted doesn't depend on the length of the rope.

3. Jul 16, 2011

### symphwar

Thanks so much! I was worried about missing something there.