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.