Question

A $200$ Hz wave with amplitude $1$ mm travels on a long string of linear mass density $6$ g/m kept under a tension of $60$N. Find the average power transmitted across a given point on the string.

Answer 1

We know that power is given by

$P=\frac{1}{2}\mu {\omega }^2{A}^{2}v$

where $\mu =6g/m=6\times {10}^{-3}kg/m$

$\omega =2\pi f=400\pi rad/s$

$A=1mm={10}^{-3}m$

$v=\sqrt{\frac{T}{\mu }}=\sqrt{\frac{60}{.006}}=100m/s$

$⟹P=\frac{1}{2}\times 6\times {10}^{-3}\times (400\pi {)}^2\times ({10}^{-3})\times 100$

$⟹P=0.4W$