A sinusoidal transverse wave travel on a string. The string has length `8.00m` and mass `6.00 g`. The wave speed is `30.0 m//s` and the wavelength is `0.200 m`. (a) If the wave is to have an average power of `50.0 W`, what must be the amplitude of the wave? (b) For the same string, if the ampitude and wavelength are the same as in part (a) what is the average power for the wave if the tension is increased such that the wave speed is doubled?

Answer

A, B, C, D

Explanation

(a) `P = (1)/(2)rhoomega^(2)A^(2)Sv`
or `A =(1)/(omega)sqrt((2P)/(rhoSv))` …(i)
Here, `rhoS =mu =` mass per unit length
`= (6xx10^(-3))/(8) kg//m`
`omega = 2pif = (2piv)/(lambda)`
`= (2pi xx 30)/(0.2)`
Substituting these values in Eq. (i), we have
`A = (0.2)/(2pi xx 30)sqrt((2 xx 50 xx 8)/(6 xx 10^(-3) xx 30))`
`= 0.0707m`
`= 7.07 cm`
`P prop vomega^(2)`
or `P prop v(v^(2))`
or `P prop v^(3)`
When wave speed is doubled, then power will become eight times.