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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. |
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Answer» Correct Answer - 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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