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A steel of length 1m, mass 0.1 kg and uniform cross – sectional area 10 -6 m 2 is rigidly fixed at both ends. The temperature of the wire is lowered by 20° C. If transverse waves are set up by plucking the string in the middle, calculate the frequency of the fundamental mode of vibration. Given for steel Y = 2 x 10 11 N/m 2 Α = 1.21 x 10 -5 per °C

A steel of length 1m, mass 0.1 kg and uniform cross – sectional area 10-6 m2 is rigidly fixed at both ends. The temperature of the wire is lowered by 20° C. If transverse waves are set up by plucking the string in the middle, calculate the frequency of the fundamental mode of vibration.
 
Given for steel Y = 2 x 1011 N/m2
Α = 1.21 x 10-5 per °C      

Grade:11

1 Answers

Aditi Chauhan
askIITians Faculty 396 Points
6 years ago
Hello Student,
Please find the answer to your question
KEY CONEPT: Using the formula of the coefficient of linear expansion,
∆ℓ = ℓα x ∆θ
Also, Y = stress/strain = T/A/∆ℓ/ℓ = T/A/α A θ ∴ T = YA α ∆θ
The frequency of the fundamental mode of vibration.
v = 1/2ℓ √T/m = 1/2ℓ √YA α ∆ θ/m
= 2/2 x 1 √2 x 1011 x 10-6 x 1.21 x 10-5 x 20/0.1 = 11 Hz..

Thanks
Aditi Chauhan
askIITians Faculty

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