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A 200 Hz wave with amplitude 1 mm travel...

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.

Text Solution

Verified by Experts

The correct Answer is:
A, B, D
(a) As derived in above problem, power
`=2pi^(2)f^(2)A^(2) sqrt(Tmu)`
`=(2) (pi)^(2)(200)^(2)(10^(-3))^(2)`sqrt(60xx(0.006))`
`=0.47 W`
(b) Energy density, `u =(1)/(2)rhoomega^(2)A^(2)`
Total energy `=(u)(V)`
`=((1)/(2)rhoomega^(2)A^(2)) (IS)`
But, `rhoS = mu`
`:.` Total energy `=(1)/(2)mul(2pif)^(2)A^(2)`
`=2pi^(2)f^(2)A^(2)mul`
`=(2)(pi)^(2)(200)^(2)(10^(-3))^(2)(0.006)(2.0)`
`=9.4 xx 10^(-3)J= 9.4 mJ`
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