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?
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?