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MHT CET 2021 (22 Sep, Shift 1) · Organ Pipes & Resonance Tube

Organ Pipes & Resonance Tube question from MHT CET 2021 (22 Sep, Shift 1)

Q91MHT CET 2021 · 22 SEP · SHIFT 1Difficult

Organ Pipes & Resonance Tube

A pipe open at both ends of length 1.5 m is dipped in water such that the second overtone of vibrating air column is resonating with a tuning fork of frequency 330 Hz. If speed of sound in air is 330 m/s then the length of the pipe immersed in water is (Neglect and correction)

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Answer: (b)

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 (b) 0.25 m.

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