Question

A stretched rope having linear mass density $5\times {10}^{-2}kg{m}^{-1}$ is under a tension of $80N$. The power that has to be supplied to the rope to generate harmonic waves at a frequency of $60Hz$ and an amplitude of $6cm$ is

• A. $215W$
• B. $251W$
• C. $512W$
• D. $521W$

Answer 1

Answer: (C)

$512W$

We know that

velocity $v=\sqrt{\frac{T}{\mu }}=\sqrt{\frac{80}{5\times {10}^{-2}}}=40m{s}^{-1}$
Power $P=\frac{1}{2}\mu {\omega }^2{A}^{2}V$
$=2{\pi }^2\mu V{A}^2{f}^2$
$=2{\pi }^2\times 5\times {10}^{-2}\times 40\times 36\times {10}^{-2}\times (60{)}^2$
$\approx 512W$