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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 10 11 N/m 2 . Coefficient of linear expansion of copper = 1.7 x 10 -5 ° C -1 . Density of copper = 9 x 10 3 kg/m 3

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

Grade:11

3 Answers

Aditi Chauhan
askIITians Faculty 396 Points
9 years ago
Hello Student,
Please find the answer to your question
(a) 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 1011 x 1.7 x 10-5 x 20/9 x 103 = 70 m/s

Thanks
Aditi Chauhan
askIITians Faculty
Shiv
19 Points
6 years ago
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
Yash Chourasiya
askIITians Faculty 256 Points
3 years ago
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

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