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MHT CET 2023 (10 May, Shift 1) · Organ Pipes & Resonance Tube

Organ Pipes & Resonance Tube question from MHT CET 2023 (10 May, Shift 1)

Q74MHT CET 2023 · 10 MAY · SHIFT 1Medium

Organ Pipes & Resonance Tube

An open organ pipe having fundamental frequency (n) is in unison with a vibrating string. If the tube is dipped in water so that $75\%$ of the length of the tube is inside the water then the ratio of fundamental frequency of the air column of dipped tube with that of string will be (Neglect end corrections)

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Answer: (b)

Open pipe: $n = \frac{v}{2L}$ = string frequency.
Dipped 75%: closed pipe of length $\frac{L}{4}$ , fundamental $= \frac{v}{4 \cdot L/4} = \frac{v}{L} = 2n$ .
Ratio $2n : n = 2 : 1$
So the answer is (b) $2:1$ .

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