A closed organ pipe of length L and an open… - JEE Main 2021 Physics PYQ

JEE Main 2021 — Physics Waves & Oscillations

2021integerhard

A closed organ pipe of length $L$ and an open organ pipe contain gases of densities ${\rho }_{1}$ and ${\rho }_{2}$ respectively. The compressibility of gases are equal in both the pipes. Both the pipes are vibrating in their first overtone with same frequency. The length of the open pipe is $\frac{x}{3}L\sqrt{\frac{{\rho }_{1}}{{\rho }_{2}}}$ , where $x$ is _______.

(Round off to the Nearest Integer)

Official previous-year question

Held on 16 Mar 2021 · Verified 6 Jul 2026.

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Solution

JEE Main 2021 Physics, Waves and Sound — solution figure

${f}_{c}={f}_{0}$

$\frac{3{V}_{C}}{4L}=\frac{2{V}_{0}}{2{L}^{'}}$

$\frac{3{V}_{C}}{4L}=\frac{{V}_{0}}{{L}^{'}}$

${L}^{'}=\frac{4L}{3}\frac{{V}_{0}}{{V}_{C}}=\frac{4L}{3}\sqrt{\frac{B.{\rho }_{1}}{{\rho }_{2}.B}}$ ( $B$ is bulk modulus)

$=\frac{4L}{3}\sqrt{\frac{{\rho }_{1}}{{\rho }_{2}}}$

$x=4$

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