A string having mass/length `1gm//m` is having a tension of 40N. A transverse wave is generated in it which has a frequency of 100Hz and amplitude of 1mm. What is the average rate at which energy is flowing through any cross section?

Options

A. `pi^(2)xx10^(-3) W`
B. `2pi^(2)xx10^(-3) W`
C. `4pi^(2)xx10^(-3) W`
D. `8pi^(2)xx10^(-3) W`

Answer

C

Explanation

`P=1/2 mu v A^(2) w^(2)`
`=1/2 xx10^(-3) xxsqrT(40/(10^(-3))) xx10^(-6) xx4pi^(2) xx10^(4)`
`=1/2 xx10^(-3) xx200xx10^(-2) xx4pi^(2)`
`=4pi^(2) xx10^(-3) W`