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A metallic rod of length 1 m , Young's modulus 3 × 10 11 N m - 2 and density 7 . 5 × 10 2 kg m - 3 is clamped at its middle. Longitudinal stationary vibrations are produced in the rod with total number of displacement nodes equal to 3 . The frequency of vibrations is

Options

  1. A30 , 000   Hz
  2. B10 , 000 Hz
  3. C3000 Hz
  4. D1500 Hz

Correct answer

A. 30 , 000   Hz

Step-by-step solution

l = 3 λ 2 ⇒ λ = 2 l 3 f = ν λ = 3 ν 2 l = 3 2 l Y ρ = 3 2 × 1 3 × 1 0 11 3 4 × 1 0 3 = 3 2 4 × 1 0 8 = 3 2 × 2 × 1 0 4 H z = 30,000 Hz

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