Organ Pipes & Resonance Tube question from MHT CET 2019 (3 May, Shift 1)

Answer: (c)

1. Open pipe $p$th overtone = $(p+1)$th harmonic: $\frac{(p+1)v}{2L}$.
2. Closed pipe $p$th overtone = $(2p+1)$th harmonic: $\frac{(2p+1)v}{4L}$.
3. Ratio $= \frac{(p+1)/2}{(2p+1)/4} = \frac{2(p+1)}{2p+1}$
4. So the answer is (c) $\frac{2(p+1)}{2p+1}$.