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MHT CET 2025 (21 Apr, Shift 1) · Organ Pipes & Resonance Tube

Organ Pipes & Resonance Tube question from MHT CET 2025 (21 Apr, Shift 1)

Q45MHT CET 2025 · 21 APR · SHIFT 1Difficult

Organ Pipes & Resonance Tube

A pipe open at both ends of length 1.5 m is dipped in water at one end such that $2$ nd overtone of vibrating air column is resonating with a tuning fork of frequency 330 Hz. The length of the pipe immersed in water is (Speed of sound in air $= 330\text{ m/s}$ ) (Neglect end correction)

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Answer: (d)

Dipped in water, the pipe acts as a closed pipe of air length $l$
2nd overtone of closed pipe = 5th harmonic: $f = \frac{5v}{4l}$
$330 = \frac{5 \times 330}{4l} \Rightarrow l = 1.25\text{ m}$
Immersed length $= 1.5 - 1.25 = 0.25\text{ m}$
So the answer is (d) 0.25 m.

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