A steel wire has a mass of `50 g//m` and is under tension 450N.
(a) Find the maximum average power that can be carried by the transverse wave in the wire if the amplitude not to exceed 20% of the wavelength. (b) The change in maximum average power if the mass per unit length of the wire is doubled. `(Use pi^(2)~=10.)`

Explanation

`v=sqrt(450/(50xx10^(-3)))=30sqrt10 m//s`
(a) the average power that can be carried by the transverse wave in wire is `P_(av)=2pi^(2)muVA^(2)f^(2)`
If the amplitude `A` equals to `20%` of wavelength `lambda`, then
`A=0.2 lambda`
The maximum power
`P_(A)=2pi^(2)muV(0.2lambda)^(2)f^(2)=0.8muv^(3)=1080sqrt(10)W`
(b) `p prop muV=mu sqrt(T)/(mu)=sqrt(T)/(mu)`
`implies p prop sqrt(mu)`
so if `mu` doubled, power becomes `sqrt(2)` times.