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 that of closed pipe is made 3 times the original, the number of beats produced will be (Neglect end correction) (a) 14 (b) 17 (c) 18 (d) 12

Answer: (b). First overtone: closed 3v/4L, open v/L; beats v/4L = 3 ⇒ v/L = 12. Open pipe L/3, fundamental: 3v/2L = 18 Hz Closed pipe 3L, fundamental: v/12L = 1 Hz Beats = 18 - 1 = 17. So the answer is (b) 17.

The closed and open organ pipe have same length and when they are… | MHT CET 2025 (20 Apr, Shift 2)

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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 $\left(\frac{1}{3}\right)^{\text{rd}}$ and that of closed pipe is made 3 times the original, the number of beats produced will be (Neglect end correction)

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Answer: (b)

First overtone: closed $\frac{3v}{4L}$ , open $\frac{v}{L}$ ; beats $\frac{v}{4L} = 3 \Rightarrow \frac{v}{L} = 12$ .
Open pipe $\frac{L}{3}$ , fundamental: $\frac{3v}{2L} = 18$ Hz
Closed pipe $3L$ , fundamental: $\frac{v}{12L} = 1$ Hz
Beats $= 18 - 1 = 17$ . So the answer is (b) 17.

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