For sound waves, if the number of nodes for the 5 th harmonic of an… | NEET 2026 (Re-neet)

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Organ Pipes & Resonance Tube

For sound waves, if the number of nodes for the $5$ th harmonic of an open-ended pipe is $n$ and that for the $9$ th harmonic of the same pipe with one of its ends closed is $m$ , the ratio $\frac{n}{m}$ is

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Answer: (d)

Open pipe, $k$ th harmonic: $L = k\frac{\lambda}{2}$ with antinodes at both ends, so it has $k$ displacement nodes. 5th harmonic: $n = 5$ .
Closed pipe, $(2k-1)$ th harmonic: $L = (2k-1)\frac{\lambda}{4}$ has $k$ nodes (one at the closed end). 9th harmonic: $2k-1 = 9 \Rightarrow m = 5$ .
$\frac{n}{m} = \frac{5}{5} = 1$
So the answer is (d) 1.

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