## waves: find amplitude, given average power

1. The problem statement, all variables and given/known data
A sinusoidal transverse wave travels on a string. The string has length 7.60 m and mass 6.50 g. The wave speed is 34.0 m/s and the wavelength is 0.250 m.
If the wave is to have an average power of 55.0 W, what must be the amplitude of the wave?
2. Relevant equations

Average Power = 0.5 * sqrt( u F ) * w^2 * A^2 where:
u = density of string, F =force, w = angular velocity, A = amplitude

3. The attempt at a solution

I put in u = (6.50*10^-3)/(0.25) = 8.55 * 10^-4
F =v^2 * u = (34)^2 * (8.55 * 10^-4 )
w = 2*pi* f = 2*pi* v/lambda = 2*3.14*(34)/(0.25)
and solved for A, and got the wrong answer (A = 2.104 m).
Where have I gone wrong?

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Hi wayfarer,

 Quote by wayfarer 1. The problem statement, all variables and given/known data A sinusoidal transverse wave travels on a string. The string has length 7.60 m and mass 6.50 g. The wave speed is 34.0 m/s and the wavelength is 0.250 m. If the wave is to have an average power of 55.0 W, what must be the amplitude of the wave? 2. Relevant equations Average Power = 0.5 * sqrt( u F ) * w^2 * A^2 where: u = density of string, F =force, w = angular velocity, A = amplitude 3. The attempt at a solution I put in u = (6.50*10^-3)/(0.25) = 8.55 * 10^-4
I think there is an error here; you are using the total mass of the string, so you need to put in the total length of the string (not the wavelength of the wave). But I guess that is just a typo in your post, because you have the right answer for $\mu$ so you did really divide by 7.6 m?

Can you give some more details (what you got for the intermediate values F, w, etc.). I did not get 2.104 m from your numbers, but it's difficult to tell where you might have gone wrong without more details.