(adsbygoogle = window.adsbygoogle || []).push({}); 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 uvA^{2}w^{2}

(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?

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# Power of a transverse wave related to rope length

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