The ratio of the speed of sound in nitrogen gas to that in helium gas, at $300 \mathrm{K}$ is

Speed of sound in an ideal gas is given by

       $v=\sqrt{\frac{\gamma RT}{M}}$

$\therefore v\propto \sqrt{\frac{\gamma }{M}}$      [$T$ is same for both the gases]

      ${\gamma }_{{\text{N}}_2}=\frac{7}{5}$        (Diatomic)

      ${\gamma }_{\text{He}}=\frac{5}{3}$        (Monoatomic)

$\therefore \frac{v_{{\text{N}}_2}}{v_{\text{He}}}=\sqrt{\frac{{\gamma }_{{\text{N}}_2}}{{\gamma }_{\text{He}}}·\frac{M_{\text{He}}}{M_{{\text{N}}_2}}}=\sqrt{\frac{7/5}{5/3}\left(\frac{4}{28}\right)}$

             $=\frac{\sqrt{3}}{5}$