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Organ Pipes & Resonance Tube question from NEET 2023

Q71NEET 2023Medium

Organ Pipes & Resonance Tube

The $4$ th overtone of a closed organ pipe is same as that of $3$ rd overtone of an open pipe. The ratio of the length of the closed pipe to the length of the open pipe is:

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Answer: (c)

Closed pipe 4th overtone = 9th harmonic: $\frac{9v}{4L_c}$ .
Open pipe 3rd overtone = 4th harmonic: $\frac{4v}{2L_o} = \frac{2v}{L_o}$ .
$\frac{9v}{4L_c} = \frac{2v}{L_o} \Rightarrow L_c : L_o = 9 : 8$
So the answer is (c) $9:8$ .

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