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MHT CET Medical202621 April 2026Evening ShiftPhysicsWaves and SoundActual

An organ pipe p₁ closed at one end has vibrating air column in its first overtone and another pipe P₂ open at both ends has vibrating air column in the third overtone, are in resonance with a given tuning fork. The ratio of the length of pipe P₁ to that of P₂ is

Options

  1. A1 : 8
  2. B3 : 8
  3. C5 : 8
  4. D1 : 2

Correct answer

B. 3 : 8

Step-by-step solution

For pipe P₁ (closed at one end), the frequency of the first overtone corresponds to the third harmonic. Its frequency is given by: f₁ = 3v 4L₁ For pipe P₂ (open at both ends), the frequency of the third overtone corresponds to the fourth harmonic. Its frequency is given by: f₂ = 4v 2L₂ Since both pipes are in resonance with the same tuning fork, their frequencies must be equal: f₁ = f₂ 3v 4L₁ = 4v 2L₂ 3 4L₁ = 2 L₂ L₁ L₂ = 3 8 The ratio of the length of pipe P₁ to that of P₂ is 3 : 8 . Answer: 3 : 8

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