An organ pipe filled with a gas at 27 ° C resonates at 400 Hz in its fundamental mode. If it is filled with the same gas at 90 ° C, the resonance frequency at the same mode will be (a) 512 Hz (b) 420 Hz (c) 440 Hz (d) 484 Hz

Answer: (c). Pipe length fixed, so f ∝ v ∝ √(T). f' = 400√((363)/(300)) = 400 × 1.1 = 440 Hz So the answer is (c) 440 Hz.

An organ pipe filled with a gas at 27 ° C resonates at 400 Hz in its… | NEET 2022 (Phase 2)

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Speed of Waves

An organ pipe filled with a gas at 27 $^\circ$ C resonates at 400 Hz in its fundamental mode. If it is filled with the same gas at 90 $^\circ$ C, the resonance frequency at the same mode will be

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Answer: (c)

Pipe length fixed, so $f \propto v \propto \sqrt{T}$ .
$f' = 400\sqrt{\dfrac{363}{300}} = 400 \times 1.1 = 440$ Hz
So the answer is (c) 440 Hz.

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