When open pipe is closed from one end third overtone of closed pipe is higher in frequency by 150 Hz, then second overtone of open pipe. The fundamental frequency of open end pipe will be (a) 400 Hz (b) 200 Hz (c) 500 Hz (d) 300 Hz

Answer: (d). Open pipe of length L: fundamental n = v/2L, second overtone = 3n. Closed from one end (same L): fundamental v/4L = n/2, third overtone = 7 × n/2 = 3.5n. 3.5n - 3n = 150 ⇒ 0.5n = 150 ⇒ n = 300 Hz So the answer is (d) 300 Hz.

When open pipe is closed from one end third overtone of closed pipe… | MHT CET 2020 (16 Oct, Shift 1)

Q97MHT CET 2020 · 16 OCT · SHIFT 1Medium

Organ Pipes & Resonance Tube

When open pipe is closed from one end third overtone of closed pipe is higher in frequency by $150\text{ Hz}$ , then second overtone of open pipe. The fundamental frequency of open end pipe will be

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Answer: (d)

Open pipe of length $L$ : fundamental $n = \frac{v}{2L}$ , second overtone $= 3n$ .
Closed from one end (same $L$ ): fundamental $\frac{v}{4L} = \frac{n}{2}$ , third overtone $= 7 \times \frac{n}{2} = 3.5n$ .
$3.5n - 3n = 150 \Rightarrow 0.5n = 150 \Rightarrow n = 300$ Hz
So the answer is (d) 300 Hz.

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