Question

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

• A. $0.63\text{W}$
• B. $0.83\text{W}$
• C. $0.47\text{W}$
• D. $0.89\text{W}$

Answer 1

The correct option is C $0.47\text{W}$

The average power transmitted across a given point in the string is $P_{average}=2{\pi }^2\mu x_0^2{f}^{2}v$
Here $v=\sqrt{\frac{T}{\mu }}=\sqrt{\frac{60}{6\times {10}^{-3}}}=100{\text{ms}}^{-1}$

$P=2\times {\pi }^2(6\times {10}^{-3})\left({10}^{-6}\right)(2\times {10}^2{)}^2\times 100$
$P=0.47\text{W}$.