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Set up a relation between speed of sound in a gas and root mean square velocity of the molecules of that gas.

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Speed of sound in a gas is \(v=\sqrt{\frac{\gamma P}{ρ}}\)(i)

According to kinetic theory of gases, root mean square velocity (c) of molecules of gas is obtained from the relation

\(P=\frac{1}{3}ρc^2,\)  \(c = \sqrt{\frac {3P}{ρ}}\)(ii)

Dividing (i) by (ii)

\(\frac{v}{c}=\sqrt{\frac{\gamma}{3}}\) 

Or  \(v=c \sqrt{\frac{\gamma}{3}}\) 

This is the required solution.

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