For a certain organ pipe, the first three resonance frequencies are in the ratio of 1: 3: 5 respectively. If the frequency of fifth harmonic is 405 Hz and the speed of sound in air is 324 ms⁻¹ the length of the organ pipe is _________ m. Numerical answer type. Work it out, then open the answer.

Answer: 1. Ratio 1: 3: 5 means odd harmonics only, so it is a closed pipe: fn = nv/4L. Fifth harmonic: 5v/4L = 405 ⇒ f₀ = 81 Hz L = v/4f₀ = (324)/(4 × 81) = 1 m So the length is 1 m.

For a certain organ pipe, the first three resonance frequencies are… | JEE Main 2023 (12 Apr, Shift 1)

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Organ Pipes & Resonance Tube

For a certain organ pipe, the first three resonance frequencies are in the ratio of $1 : 3 : 5$ respectively. If the frequency of fifth harmonic is $405\text{ Hz}$ and the speed of sound in air is $324\text{ ms}^{-1}$ the length of the organ pipe is _________ $\text{m}$ .

Numerical answer type. Work it out, then open the answer.

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Answer: 1

Ratio $1 : 3 : 5$ means odd harmonics only, so it is a closed pipe: $f_n = \frac{nv}{4L}$ .
Fifth harmonic: $\frac{5v}{4L} = 405 \Rightarrow f_0 = 81\text{ Hz}$
$L = \frac{v}{4f_0} = \frac{324}{4 \times 81} = 1\text{ m}$
So the length is $1\text{ m}$ .

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