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An organ pipe P₁ closed at one end vibrating in its first overtone and another pipe P₂ open at both ends vibrating in its third overtone are in resonance with a given tuning fork. The ratio of lengths of P₁ and P₂ respectively are given by

1. 1 : 2
2. 1 : 3
3. 3 : 8
4. 3 : 4

Correct answer: 3 : 8

Solution

For a pipe closed at one end (P₁), the first overtone corresponds to the third harmonic, where the length is L₁ = 3λ/4. For a pipe open at both ends (P₂), the third overtone corresponds to the seventh harmonic, where the length is L₂ = 7λ/4. The ratio of lengths is L₁/L₂ = 3/8.

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