A closed organ pipe of length ' L₁ ' and an open organ pipe contain… | MHT CET 2023 (9 May, Shift 1)

Q75MHT CET 2023 · 9 MAY · SHIFT 1Difficult

Organ Pipes & Resonance Tube

A closed organ pipe of length ' $L_1$ ' and an open organ pipe contain diatomic gases of densities ' $\rho_1$ ' and ' $\rho_2$ ' respectively. The compressibilities of the gases are same in both pipes, which are vibrating in their first overtone with same frequency. The length of the open organ pipe is (Neglect end correction)

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Answer: (b)

Speed $v = \sqrt{\frac{B}{\rho}}$ ; same $B$ , so $\frac{v_2}{v_1} = \sqrt{\frac{\rho_1}{\rho_2}}$
Closed pipe first overtone: $\frac{3v_1}{4L_1}$ ; open pipe first overtone: $\frac{v_2}{L_o}$
Equate: $L_o = \frac{4L_1}{3}\frac{v_2}{v_1} = \frac{4L_1}{3}\sqrt{\frac{\rho_1}{\rho_2}}$
So the answer is (b).

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