A closed organ pipe of length ' Lc ' and an open organ pipe of length… | MHT CET 2021 (21 Sep, Shift 1)

Q93MHT CET 2021 · 21 SEP · SHIFT 1Difficult

Organ Pipes & Resonance Tube

A closed organ pipe of length ' $L_c$ ' and an open organ pipe of length ' $L_o$ ' contain different gases of densities ' $\rho_1$ ' and ' $\rho_2$ ' respectively. The compressibility of the gases is the same in both the pipes. The gases are vibrating in their first overtone with the same frequency. What is the length of open organ pipe?

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Answer: (a)

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

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