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MHT CET 2021 (24 Sep, Shift 2) · Beats

Beats question from MHT CET 2021 (24 Sep, Shift 2)

Q52MHT CET 2021 · 24 SEP · SHIFT 2Medium

Beats

A closed organ pipe and an open 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 now halved and that of closed pipe is doubled. The number of beats produced per second will be

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Answer: (d)

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

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