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`?

Explanation

The wave speed on the string is
`v = sqrt((T)/(mu)) =((80.0N)/(5.00xx10^(-2)kg//m))^(1//2) = 40.0 m//s`
Because ` f = 60Hz`, the angular frequency `omega` of the sinusoidal wave on the string has the value
`omega = 2pif =2pi (60.0Hz) = 377 s^(-1)`
Using these values in following equation for the power, with A = ` 6.00 xx 10^(-2)`m, 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`.