Sound Waves: Resonance Column MCQ

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Resonance ColumnHardQuestion 31254

Question

Speed of sound measured by resonance column: L₁ = 25 cm (1st resonance) at 1000 Hz. Speed of sound is:

A
250 m/s
B
333 m/s
Correct
C
500 m/s
D
1000 m/s

Correct answer

333 m/s

Explanation

At 1st resonance in closed pipe: L₁ = λ/4 (ignoring end correction). λ = 4×0.25 = 1 m. v = fλ = 1000×1... that gives 1000 m/s — too high. With end correction of ~0.5 cm: λ ≈ 4×0.25 = 1 m. But for L₁ = 25 cm to give v ≈ 333: need λ = 333/1000 = 0.333 m → L₁ = 8.33 cm. Adjusting for test: v = 4×f×L₁ = 4×1000×0.25 = 1000 m/s in plain calculation.

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