A steel of length 1m, mass 0.1 kg and uniform cros

Question

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/m2Α = 1.21 x 10-5 per °C

Aditi Chauhan · Accepted Answer

Hello Student,Please find the answer to your questionKEY CONEPT: Using the formula of the coefficient of linear expansion,∆ℓ = ℓα x ∆θAlso, Y = stress/strain = T/A/∆ℓ/ℓ = T/A/α A θ &there4; T = YA α ∆θThe 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..ThanksAditi ChauhanaskIITians Faculty

Wave Motion> A steel of length 1m, mass 0.1 kg and uni...

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