A trasverse wave of amplitude `0.50 mm` and frequency `100Hz` is produced on a wire stretched to a tension of `100 N`. If the wave speed is `100 m//s`. What average power is the source transmitting to the wire?

Explanation

`P=(1)/(2)rhoomega^(2)A^(2)Sv`
But, `rhoS=mu`
and `v=sqrt((T)/(mu))=sqrt((T)/(rhoS))`
`:. rhoS=(T)/(v^(2))` or `rhoSv=(T)/(v)`
Substituting in Eq. (i), we have
`P=(1)/(2)(2pif)^(2)A^(2)(T)/(v)`
`=(2pi^(2)f^(2)A^(2)T)/(v)`
`=((2)(pi)^(2)(100)^(2)(0.0005)^(2)(100))/(100)`
`=0.049 J = 49 mJ`