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MHT CET 2025 (19 Apr, Shift 1) · Organ Pipes & Resonance Tube

Organ Pipes & Resonance Tube question from MHT CET 2025 (19 Apr, Shift 1)

Q40MHT CET 2025 · 19 APR · SHIFT 1Medium

Organ Pipes & Resonance Tube

The frequency of fourth overtone of a closed pipe is in unison with the fifth overtone of an open pipe. The ratio of length of closed pipe to that of open pipe is

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Answer: (b)

Closed pipe, fourth overtone (9th harmonic): $\frac{9v}{4L_c}$ .
Open pipe, fifth overtone (6th harmonic): $\frac{6v}{2L_o} = \frac{3v}{L_o}$ .
$\frac{9}{4L_c} = \frac{3}{L_o} \Rightarrow \frac{L_c}{L_o} = \frac{9}{12} = \frac{3}{4}$
So the answer is (b) $3 : 4$ .

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