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
- A1 : 8
- B3 : 8
- C5 : 8
- 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