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A taut string for which mu = 5.00 xx 10^...

A taut string for which `mu = 5.00 xx 10^(-2) kg//m` under a tension of `80.0N`. How much power must be supplied to the string to generate sinusoidal waves at a frequency of `60.0 Hz` and an amplitude of `6.00 cm`?

Text Solution

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The wave speed on the string is
`v = sqrt((T)/(mu)) = ((80.0N)/(5.00 xx 10^(-2)kg//m))^(1//2) = 40.0 m//s`
Because `phi = 60 Hz`, the anguler frequency `omega` of the sinusoidal waves on the string has the value
`omega = 2pif = 2pi(60.0 Hz) = 377 s^(-1)`
Using these values in following Equation for the power, with `A = 6.00 xx 10^(-2)`,. Gives
`p = (1)/(2) muomega^(2)A^(2)v`
`= (1)/(2) (5.00 xx 10^(-2) kg//m)(377s^(-1))^(2) xx (6.00 xx 10^(-2)m)^(2)(40.0 m//s)`
`= 512 W`.
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