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At a given temperature if $V_{rms}$ is the root mean square velocity of the molecules of a gas, $V_{s}$ is the velocity of sound in it, then these are related as: $(γ = \frac{C_{p}}{C_{v}})$

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$V_{r m s} = V_{s}$

$V_{r m s} = \sqrt{\frac{3}{γ}} \times V_{s}$

$V_{r m s} = \sqrt{\frac{γ}{3}} \times V_{s}$

$V_{r m s} = (\frac{3}{γ}) \times V_{s}$

answer is B.

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Detailed Solution

$\begin{matrix} V_{r m s} = \sqrt{\frac{3 R T}{M}} \\ V_{S} = \sqrt{\frac{γ R T}{M}} \end{matrix}$

$∴ \frac{V_{r m s}}{V_{S}} = \sqrt{\frac{3}{γ}} .$

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