Waves

JEE Main level, single correct, medium

76 of 142

Question 76 of 142

A sonometer wire of length 1.5m1.5m is made of steel. The tension in it produces an elastic strain of \text{1%}. What is the fundamental frequency of steel if density and elasticity of steel are 7.7×103kgm−37.7\times {10}^{3}kg{m}^{-3} and 2.2×1011Nm−22.2\times {10}^{11}N{m}^{-2} respectively?

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Answer: (D) 178.2Hz178.2Hz

ff = VV 2 ℓ = 1 2 ℓ TT μ = 1 2 ℓ TT AdAd

Also, YY = TT ℓ AA Δ ℓ ⇒ TT AA = YY Δ ℓ ℓ ⇒ ff = 1 2 ℓ Y Δ ℓ ℓ d

ℓ=1.5 m,Δℓℓ=0.01, d=7.7×103kg/m3\ell =\text{1.5 m,}\dfrac{\Delta \ell }{\ell }=\text{0.01, d}=\text{7.7}\times 1{0}^{3}\text{kg}/{\text{m}}^{3}

Y=2.2×1011N/m2\text{Y}=\text{2.2}\times 1{0}^{11}\text{N}/{\text{m}}^{2}

After solving

ff = 2 7 × 1 0 3 3 Hz\text{H}\text{z}

ff ≈ 178.2 Hz\text{H}\text{z}

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