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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
10 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
7 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
4 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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