Two organ pipes, each closed at one end, give 6 beats per s, when emitting their fundamental nodes. If their lengths are in the ratio of 6: 5, their fundamental frequencies (in Hz) are f₁ and f₂ then find the value of f₁ + f₂:
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Question

Two organ pipes, each closed at one end, give 6 beats per s, when emitting their fundamental nodes. If their lengths are in the ratio of 6: 5, their fundamental frequencies (in Hz) are f₁ and f₂ then find the value of f₁ + f₂:

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G1 Physics · Accepted Answer

Step 1: Open-open pipe: fₙ = nv/(2effective length). Closed-open pipe: fₙ = (2n−1)v/(4effective length). Step 2: Include end correction in effective length where stated; successive resonances differ by λ/2. Step 3: Apply the harmonic/resonance condition. Final: A: 66.