Solving Frequency of Harmonic Wave Problem

[zhartman]

Homework Statement

A 2.12-m long rope has a mass of 0.116 kg. The tension is 62.9 N. An oscillator at one end sends a harmonic wave with an amplitude of 1.09 cm down the rope. The other end of the rope is terminated so all of the energy of the wave is absorbed and none is reflected. What is the frequency of the oscillator if the power transmitted is 118 W?

Homework Equations

$V_{wave}=f\lambda$
$V_{wave string}=\sqrt{\frac{\tau}{\frac{m}{L}}}$
$\omega=\frac{2pi}{T}=2\pi*f$
$P=(\frac{1}{2})(\mu)(V_{wave})(\omega)^2(A)^2$

The Attempt at a Solution

Using the Power equation I plugged in the general form for $v_{wave}$ as well as the general for $\omega$. Since there is no wavelength given and one harmonic wave is passing I plugged in L for $\lambda$, giving me;
$P=(\frac{1}{2})\sqrt{\frac{\tau}{\frac{m}{L}}}(fL)(4*\pi^2*f^2)(A)^2$

Solving for f:

$f^3=\frac{2P}{4\pi^2A^2L\sqrt{\frac{\tau}{\frac{m}{L}}}}$

I'm not sure where I am going wrong in this; I believe all of my algebra is correct. Does it have something to do with $(\lambda)\neq(L)$ here.

 

[Simon Bridge]

Yes = $\lambda \neq L$