Question

A steel wire has a mass of $5g/m$ and is under tension $450N$. The maximum average power that can be carried by the transverse wave in the wire if the amplitude is not to exceed $20\%$ of the wavelength is $x\times {10}^{4}W$. Find $x$.

Answer 1

Velocity$\left(v\right)=\sqrt{\frac{T}{\mu }}=\sqrt{\frac{450}{5\times {10}^{-3}}}=300m{s}^{-1}$

$A_{max}=\frac{1}{5}\lambda =\frac{1}{5}\frac{v}{\nu }$

$\omega =2\pi \nu$

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

Substituting above values we get

$AveragePower=\frac{1}{2}\mu \left(2\pi {)}^2\right(\frac{v}{5}{)}^{2}v$

Solving we get $AveragePower=11\times {10}^4$

$x=11$