# Waves: find amplitude, given average power

## Homework Statement

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?

## Homework Equations

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

## 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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alphysicist
Homework Helper
Hi wayfarer,

## Homework Statement

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?

## Homework Equations

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

## 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.

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