Transverse Wave

The power transported by a string under tension is given by:

$E_\lambda = \frac 12 \mu \omega^2 A^2 v$

where $\mu$ is the linear density of the string, and $\omega$ , $A$ , and $v$ are angular frequency, amplitude, and propagating velocity of the wave. Then we have:

$\begin{aligned} E_\lambda & = \frac 12 (0.865) \blue{\omega}^2 \left(8.5 \times 10^{-3}\right)^2 \red v & \small \blue {\text{Note that }\omega = 2 \pi f \text{, where }f \text{ is the wave frequency.}} \\ & = \frac 12 (0.865) \blue{(2\pi \cdot 80)}^2 \left(0.0085\right)^2 \red{\sqrt{\frac {50}{0.865}}} & \small \red{\text{and } v = \sqrt{\frac {F_T}\mu} \text{, where }F_T\text{ is the string tension.}} \\ & \approx \boxed{60} \end{aligned}$