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For a certain organ pipe the first three resonance frequencies are in the ratio 1:3:5. If the frequency of the fifth harmonic is 405 Hz and the speed of sound in air is 324 m s⁻¹, the length of the pipe is ______ m.

Asked in JEE Main 12th April 1st Shift 2023 · Closed and open pipes

Answer: 1

Step-by-step solution

The ratio 1:3:5 shows that only odd harmonics are present, so the pipe is closed at one end.

The fifth harmonic is 5f₁=405 Hz, so f₁=81 Hz.

L=v/(4f₁)=(324)/(324)=1 m.

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