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Power supplied to a vibrating string: A ...

Power supplied to a vibrating string: A string with linear mass density `mu=5.00xx10^(-2) kg//m` is under a tension of 80.0 N. 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

Verified by Experts

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 =60 Hz`, the angular frequency `omega` of the sinusoidal waves on the string has the value
`omega=2pif=2pi(60.0Hz)=377_(s)^(-1)`
using these value in Eq. (iii)for the power, with amplitude `A=6.00xx10^(2) m`, gives
`p=(1)/(2)muomega^(2)A^(2)_(v)`
`(1)/(2)(5.00xx10^(-2)kg//m)(377 s^(-1))^(2)`
`xx(6.00xx10^(-2)m)^(2)(40.0 m//s)=512 W`
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