A one metre long (both ends open) organ… - JEE Main 2020 Physics PYQ

JEE Main 2020 — Physics Waves & Oscillations

2020integerhard

A one metre long (both ends open) organ pipe is kept in a gas that has double the density of air at STP. Assuming the speed of sound in air at STP is $300m/s,$ the frequency difference between the fundamental and second harmonic of this pipe is __________ Hz.

Official previous-year question

Held on 8 Jan 2020 · Verified 6 Jul 2026.

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Solution

$V=\sqrt{\frac{B}{\rho }}$

$\frac{{V}_{pipe}}{{V}_{air}}=\frac{\sqrt{\frac{B}{2\rho }}}{\sqrt{\frac{B}{\rho }}}=\frac{1}{\sqrt{2}}$

${V}_{pipe}=\frac{{V}_{air}}{\sqrt{2}}$

${f}_{n}=\frac{(n+1){V}_{pipe}}{2l}$

${f}_{1}-{f}_{0}=\frac{{V}_{pipe}}{2l}=\frac{300}{2\sqrt{2}}=105.75Hz(if\sqrt{2}=1.41)$

$=106.05Hz(if\sqrt{2}=1.414)$

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