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)`.

Options

A. 210 m/s
B. 110 m/s
C. 90 m/s
D. 70 m/s

Answer

D

Explanation

`DeltaL=(TL)/(AY)rArr T=(DeltaLAY)/(L)=(LalphathetaAY)/(L)=alpha thetaAy`
`mu =dA :. v=sqrt((T)/(mu))=sqrt((alpha theta AY)/(dA))=70 m//s`