An open organ pipe and closed organ pipe of same length produce 2… | MHT CET 2025 (5 May, Shift 2)

Q24MHT CET 2025 · 5 MAY · SHIFT 2Medium

Beats

An open organ pipe and closed organ pipe of same length produce 2 beats per second, when they are set into vibrations together, in fundamental mode. The length of open pipe is made half and that of closed pipe is doubled.

The number of beats produced per second will be (neglect end correction)

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Answer: (c)

Open pipe: $f_o = \frac{v}{2L}$ ; closed pipe: $f_c = \frac{v}{4L}$ .
Beats: $f_o - f_c = \frac{v}{4L} = 2 \Rightarrow \frac{v}{L} = 8$
Open pipe of length $\frac{L}{2}$ : $f_o' = \frac{v}{L} = 8$ Hz; closed pipe of length $2L$ : $f_c' = \frac{v}{8L} = 1$ Hz
Beats $= 8 - 1 = 7$ . So the answer is (c) 7.

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