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The ratio of the speed of sound in a monatomic gas at $27^{\circ} \mathrm{C}$ and rms speed of the molecules of the same gas at a temperature of $127^{\circ} \mathrm{C}$ is
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The correct answer is:
$\sqrt{5}: \sqrt{12}$
Speed of sound in gas
For monoatonic gas, $r=\frac{5}{3}$
Also, $T_1=300 \mathrm{~K}, T_2=400 \mathrm{~K}$,
$$
\begin{aligned}
& \therefore \quad \text { Ratio, } \frac{v}{c}=\sqrt{\frac{\gamma \cdot \mathrm{T}_1}{3 \cdot T_2}}=\sqrt{\frac{5 / 3 \times 300}{3 \times 400}} \\
& \quad \frac{v}{c}=\frac{\sqrt{5}}{\sqrt{12}}
\end{aligned}
$$
For monoatonic gas, $r=\frac{5}{3}$
Also, $T_1=300 \mathrm{~K}, T_2=400 \mathrm{~K}$,
$$
\begin{aligned}
& \therefore \quad \text { Ratio, } \frac{v}{c}=\sqrt{\frac{\gamma \cdot \mathrm{T}_1}{3 \cdot T_2}}=\sqrt{\frac{5 / 3 \times 300}{3 \times 400}} \\
& \quad \frac{v}{c}=\frac{\sqrt{5}}{\sqrt{12}}
\end{aligned}
$$
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