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MHT CET 2024 (11 May, Shift 2) · Organ Pipes & Resonance Tube

Organ Pipes & Resonance Tube question from MHT CET 2024 (11 May, Shift 2)

Q55MHT CET 2024 · 11 MAY · SHIFT 2Medium

Organ Pipes & Resonance Tube

The frequency of the third overtone of a pipe of length ' $L_c$ ', closed at one end is same as the frequency of the sixth overtone of a pipe of length ' $L_0$ ', open at both ends. Then the ratio $L_c : L_0$ is

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Answer: (b)

Closed pipe third overtone = 7th harmonic: $\frac{7v}{4L_c}$ .
Open pipe sixth overtone = 7th harmonic: $\frac{7v}{2L_0}$ .
$\frac{7v}{4L_c} = \frac{7v}{2L_0} \Rightarrow 4L_c = 2L_0 \Rightarrow L_c : L_0 = 1 : 2$
So the answer is (b) $1:2$ .

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