A `200 Hz` wave with amplitude `1 mm` travels on a long string of linear mass density `6 g//m` keep under a tension of `60 N`.
(a) Find the average power transmitted across a given point on the string.
(b) Find the total energy associated with the wave in a `2.0 m` long portion of the string.

Answer

A, B, D

Explanation

`A=1mm=10^-3m,`
`m=6gm=6x10^-3kg/m`
`T=60N,f=200Hz`
`V=sqrt((T/m))=sqrt((60)/(6xx10^-3))` ltBrgt `=10^2=100m/s`
`a. P_(average)=2pi^2mvA^2f^2`
`=2xx(3.14)^2xx(6xx10^-3)`
`xx100xx(10^3)xx200^2`
`=473xx10^-3=0.47W`
b. Length of the string is 2m.
So,t=2/100=0.02sec`
`Energy =2pi^2mvf^2A^2t`
`=2xx(3.14)62xx6xx(10^-3)`
xx100xx200^2xxx910^-3)^2x(0.02)`
`=946.5xx10^-5`
`=9.46xx10^-3J=9.46mJ`