Solution
= Solution
The <wave speed> is $c=\sqrt{T/\rho}=50\,\mathrm{m\,s^{-1}}$, so the <frequency> is $f=c/\lambda=100\,\mathrm{Hz}$ and $\omega=200\pi\,\mathrm{s^{-1}}$. Substituting the amplitude in metres,
$$
\boxed{\overline P=\frac12(50)(0.1)(0.005)^2(200\pi)^2
=2.5\pi^2\,\mathrm W\simeq24.67\,\mathrm W.}
$$
Power scales with the square of amplitude; converting millimetres to metres before squaring is essential.