Answer
$197\;Hz$
Work Step by Step
The average power is given by
$P_{avg}=\frac{1}{2}\mu v \omega^2 y_m^2$
or $P_{avg}=\frac{1}{2}\mu \sqrt {\frac{T}{\mu}} \omega^2 y_m^2$
or, $P_{avg}=\frac{1}{2}\sqrt {T\mu} \omega^2 y_m^2$
or, $\omega^2=\frac{2P_{avg}}{y_m^2\sqrt {T\mu}}$
Substituting the given values
or, $\omega^2=\frac{2\times85}{(7.70\times10^{-3})^2\sqrt {36\times(\frac{0.26}{2.70})}}$
or, $\omega=1241$
or, $2\pi f=1241$
or, $f=197\;Hz$
$\therefore$ The frequency of traveling waves is $197\;Hz$
