Question

A $200Hz$ wave with amplitude $1mm$ travels on a long string of linear mass of density $6g{m}^{-1}$ kept under a tension of $60N$. The average power transmitted across a given point in the string is

• A. $0.53W$
• B. $0.83W$
• C. $0.47W$
• D. $0.89W$

Answer 1

The correct option is C $0.47W$

$p_{average}=2{\pi }^2\mu x_0^2{f}^{2}v$

$v=\sqrt{\frac{T}{\mu }}=\sqrt{\frac{60}{6\times {10}^{-3}}}=100m{s}^{-1}$
$p_{average}=2\times {\pi }^2(6\times {10}^{-3})\left({10}^{-6}\right)(2\times {10}^2{)}^2\times 100=0.47W$