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A sonometer wire of length 1 .5 m is made of steel. The tension in it produces an elastic strain of 1% . What is the fundamental frequency of steel if density and elasticity of steel are 7 .7 × 10 3 kg m - 3 and 2 .2 × 10 11 N m - 2 respectively?

Options

  1. A200 .5   Hz
  2. B770   Hz
  3. C188 .5   Hz
  4. D178 .2   Hz

Correct answer

D. 178 .2   Hz

Step-by-step solution

f = V 2 ℓ = 1 2 ℓ T μ = 1 2 ℓ T A d Also, Y = T ℓ A Δ ℓ ⇒ T A = Y Δ ℓ ℓ ⇒ f = 1 2 ℓ Y Δ ℓ ℓ d ℓ = 1.5 m, Δ ℓ ℓ = 0.01, d = 7.7 × 1 0 3 kg / m 3 Y = 2.2 × 1 0 1 1 N / m 2 After solving f = 2 7 × 1 0 3 3 H z f ≈ 178.2 H z

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