A metal wire with volume density `rho` and young's modulus `Y` is stretched between rigid supports. At temperature `T`, the speed of a transverse wave is found to be `v_(1)`. When temperature decreases `T - DeltaT`, the speed increases to `v_(2)`. Datermine coefficient of linear expansion of wire.

Explanation

If temperature decreases,s tension in wire increases and `v` increases
`v_(1) = sqrt((F)/(mu))`
`F = muv_(1^(2))`
`DeltaF = YAalphaDeltaT`
`v_(2) = sqrt((F + DeltaF)/(mu)) = sqrt((F + YAalphaDeltaT)/(mu))`
`v_(2^(2)) = v_(1^(2)) + (YAalphaDeltaT)/((m//l)) = v_(2^(2)) - v_(1^(2))`
`(YalphaDeltaT)/(rho) = v_(2^(2)) - v_(1^(2))`
`alpha = (rho(v_(2^(2)) - v_(1^(2))))/(YDeltaT)`