The third overtone of a closed pipe of length ' Lc ' has the same frequency as the third overtone of the open pipe of length ' L₀ '. Both the pipes have same diameters. The ratio Lc: L₀ is equal to (a) 8: 7 (b) 7: 8 (c) 5: 3 (d) 3: 2

Answer: (b). Closed pipe, third overtone (7th harmonic): (7v)/(4Lc). Open pipe, third overtone (4th harmonic): (4v)/(2L₀) = 2v/L₀. 7/4Lc = 2/L₀ ⇒ Lc: L₀ = 7: 8 So the answer is (b) 7: 8.

The third overtone of a closed pipe of length ' Lc ' has the same… | MHT CET 2026 (19 Apr, Shift 1)

Q15MHT CET 2026 · 19 APR · SHIFT 1Medium

Organ Pipes & Resonance Tube

The third overtone of a closed pipe of length ' $L_c$ ' has the same frequency as the third overtone of the open pipe of length ' $L_0$ '. Both the pipes have same diameters. The ratio $L_c : L_0$ is equal to

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Answer: (b)

Closed pipe, third overtone (7th harmonic): $\frac{7v}{4L_c}$ .
Open pipe, third overtone (4th harmonic): $\frac{4v}{2L_0} = \frac{2v}{L_0}$ .
$\frac{7}{4L_c} = \frac{2}{L_0} \Rightarrow L_c : L_0 = 7 : 8$
So the answer is (b) $7 : 8$ .

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