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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
Detailed Solution
For both open and closed pipes, number of nodes = m + 1, where m is the number of the overtone. Open pipe: 5th harmonic = 4th overtone, so n = 4 + 1 = 5. Closed pipe: 9th harmonic = 4th overtone, so m = 4 + 1 = 5. Hence $\frac{n}{m}=\frac{5}{5}=1$.