Consider the sound wave travelling in ideal gases of He, CH_4 , and CO_2 . All the gases have the same ratio (P)/( ) , where P is the pressure and is the density. The ratio of the speed of sound through the gases v_ He

Correct answer: C. (5)/(3) : (4)/(3) : (4)/(3) aligned & v_ sound = γ p & γ=1+ 2 f & γ_ He =(5)/(3) & .γ_ CH_4 =γ_ CO_2 1.33=(4)/(3) (Experimental data ) aligned

JEE Main 20254 AprilMorning Shift

Exam: JEE Main
Year: 2025
Date: 4 April
Shift: Morning Shift
Subject: Physics
Chapter: Waves and Sound

JEE Main 2025 · 4 April · Morning Shift · Physics · Waves and Sound

Consider the sound wave travelling in ideal gases of He, CH_4 , and...

Consider the sound wave travelling in ideal gases of

\mathrm{He}, \mathrm{CH}_4

, and

\mathrm{CO}_2

. All the gases have the same ratio

\frac{P}{\rho}

, where

P

is the pressure and

\rho

is the density. The ratio of the speed of sound through the gases

\mathrm{v}_{\mathrm{He}}: \mathrm{v}_{\mathrm{CH}_4}: \mathrm{v}_{\mathrm{CO}_2}

is given by

Options

A $\sqrt{\frac{7}{5}}: \sqrt{\frac{5}{3}}: \sqrt{\frac{4}{3}}$
B $\sqrt{\frac{5}{3}}: \sqrt{\frac{4}{3}}: \sqrt{\frac{7}{5}}$
C $\sqrt{\frac{5}{3}}: \sqrt{\frac{4}{3}}: \sqrt{\frac{4}{3}}$
D $\sqrt{\frac{4}{3}}: \sqrt{\frac{5}{3}}: \sqrt{\frac{7}{5}}$

Correct answer

C. $\sqrt{\frac{5}{3}}: \sqrt{\frac{4}{3}}: \sqrt{\frac{4}{3}}$

Step-by-step solution

\begin{aligned} & \mathrm{v}_{\text{sound }}=\sqrt{\frac{\gamma \mathrm{p}}{\rho}} \\ & \gamma=1+\frac{2}{\mathrm{f}} \\ & \gamma_{\mathrm{He}}=\frac{5}{3} \\ & \left.\gamma_{\mathrm{CH}_4}=\gamma_{\mathrm{CO}_2} \approx 1.33=\frac{4}{3} \quad \text{ (Experimental data }\right)\end{aligned}

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