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AP EAMCET2010PhysicsWaves and Sound

An organ pipe P₁ , closed at one end and containing a gas of density ₁ is vibrating in its first harmonic. Another organ pipe P₂ , open at both ends and containing a gas of density ₂ is vibrating in its third harmonic. Both the pipes are in resonance with a given tuning fork. If the compressibility of gases is equal in both pipes, the ratio of the lengths of P₁ and P₂ is (assume the given gases to be monoatomic)

Options

  1. A1 3
  2. B3
  3. C1 6 ₁ ₂
  4. D1 6 ₂ ₁

Correct answer

D. 1 6 ₂ ₁

Step-by-step solution

Frequency of closed organ pipe for first harmonic n₁= v₁ 4 l₁ . Frequency of open organ pipe for third harmonic n₃= 3 v₂ 2 l₂ At resonance, n₁=n₃ or v₁ 4 l₁ = 3 v₂ 2 l₂ or l₁ l₂ = 1 6 ( v₁ v₂ ) l₁ l₂ = 1 6 B ₁ ₂ B = 1 6 ₂ ₁

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