For sound waves, let n be the number of displacement nodes in the 5th harmonic of an open-ended pipe. Let m be the number of nodes in the 9th harmonic of the same pipe when one end is closed. Find n/m.
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Question

For sound waves, let n be the number of displacement nodes in the 5th harmonic of an open-ended pipe. Let m be the number of nodes in the 9th harmonic of the same pipe when one end is closed. Find n/m.

Options

G1 Physics · Accepted Answer

Step 1: An open–open pipe has displacement antinodes at both ends. Its fifth harmonic contains five internal nodes, so n = 5. Step 2: A closed–open pipe supports odd harmonics. Its ninth harmonic corresponds to five quarter-wavelength segments and contains five nodes, including the closed end; hence m = 5. Step 3: n/m = 5/5 = 1. Final answer: 1 (Option C).