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 x 10¹¹ N/m². Coefficient of linear expansion of copper = 1.7 x 10^-5 ° C^-1. Density of copper = 9 x 10³ kg/m³

Use direct formula :v = √Ya∆T / density = √ 1.3× 10^11 × 1.7× 10^-5 × 20 ÷ 9 × 10^3= 70 m/s In words ...( whole Underroot Young`s modulus × cofficient of linear expansion × diff of temperature divided by density )Thank you

Dear Student

Using the formula of the coefficient of linear expansion of wire, ∆ℓ = ℓα∆θ we get
F = YAα∆θ
Speed of transverse wave is given by
V = √F/m [ where m = mass per unit length = Alp = Ap]
= √YAα∆θ/Ap = √Yα∆θ/p
= √1.3 x 10¹¹x 1.7 x 10^-5x 20/9 x 10³= 70 m/s

I hope this answer will help you.
Thanks & Regards
Yash Chourasiya