The closed and open organ pipe have same length and when they are vibrating simultaneously in first overtone produce 3 beats. The length of open pipe is made (1/3)rd and closed pipe is made 3 times the original, the number of beats produced will be {neglect end correction} (a) 8 (b) 10 (c) 17 (d) 14

Answer: (c). First overtone: closed fc = 3v/4L, open fo = 2v/2L = v/L. Beats: v/L - 3v/4L = v/4L = 3 ⇒ v/L = 12 New lengths, fundamental modes: open ( L/3): 3v/2L = 18 Hz; closed ( 3L): v/12L = 1 Hz Beats = 18 - 1 = 17. So the answer is (c) 17.

The closed and open organ pipe have same length and when they are… | MHT CET 2026 (11 Apr, Shift 2)

Q14MHT CET 2026 · 11 APR · SHIFT 2Difficult

Beats

The closed and open organ pipe have same length and when they are vibrating simultaneously in first overtone produce $3$ beats. The length of open pipe is made $\left(\frac{1}{3}\right)^{rd}$ and closed pipe is made $3$ times the original, the number of beats produced will be {neglect end correction}

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Answer: (c)

First overtone: closed $f_c = \frac{3v}{4L}$ , open $f_o = \frac{2v}{2L} = \frac{v}{L}$ .
Beats: $\frac{v}{L} - \frac{3v}{4L} = \frac{v}{4L} = 3 \Rightarrow \frac{v}{L} = 12$
New lengths, fundamental modes: open ( $\frac{L}{3}$ ): $\frac{3v}{2L} = 18$ Hz; closed ( $3L$ ): $\frac{v}{12L} = 1$ Hz
Beats $= 18 - 1 = 17$ . So the answer is (c) 17.

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Beats question from MHT CET 2026 (11 Apr, Shift 2)

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