A copper wire is held at the two ends by rigid supports. At `30^(@)C`, the wire is just taut, with negligible tension. Find the speed of transverse waves in this wire at `10^(@)C`.
Given : Young modulus of copper `= 1.3 xx 10^(11) N//m^(2)`.
Coefficient of linear expansion of copper ` = 1.7 xx 10^(-5) ^(@)C^(-1)`. Density of copper `= 9 xx 10^(3) kg //m^(3)`.

Explanation

(a) using the formula of the coefficient of linear expansion of wire, `Deltal = lalphaDeltatheta` we get
`F = YAalphaDelta theta`
Speed of transverse wave is given by
`v = sqrt((F)/(m)) [where`m = mass per unit length = (Alrho)/(l) = Arho]`
`= sqrt((YAalphaDeltatheta)/(Arho)) = sqrt((YalphaDeltatheta)/(rho))`
`= sqrt((1.3 xx 10^(11) xx 1.7 xx 10^(-5) xx 20)/(9 xx 10^(3))) = 70m//s`