The ratio of the speed of sound in helium gas to that in nitrogen gas at the same temperature is \(\left(\gamma_{\mathrm{He}}=\frac{5}{3}, \gamma_{\mathrm{N}_2}=\frac{7}{5}, M_{\mathrm{He}}=4, M_{\mathrm{N}_2}=28\right)\)

The correct option is (A).
Concept: Newton-Laplace equation for the speed of sound in an ideal gas is given by, \(c=\sqrt{\frac{\gamma P}{\rho}}\) where is the speed of sound, \(\gamma\) is the adiabatic index, \(P\) the pressure and \(\rho\) the density of the gas.
On introducing pressure \(P=\frac{\rho R T}{M}\) by using the ideal gas equation, the speed of sound can be written as \(c=\sqrt{\frac{\gamma R T}{M}}\). The speed of sound is proportional to the square root of the ratio of adiabatic index \(y\) and molecular weight \(\mathrm{M}\), i.e., \(c \propto \sqrt{\frac{\gamma}{M}}\). On taking the ratio for Helium
and Nitrogen: \(\frac{c_{\mathrm{He}}}{c_{\mathrm{N}_2}}=\sqrt{\frac{\gamma_{\mathrm{He}}}{M_{\mathrm{He}}} \times \frac{M_{\mathrm{N}_2}}{\gamma_{\mathrm{N}_2}}}\)
On plugging in the values: \(\frac{c_{\mathrm{He}}}{c_{\mathrm{N}_2}}=\sqrt{\frac{\frac{5}{3}}{\frac{7}{5}} \times \frac{28}{\sqrt{3}}}=\frac{5}{\sqrt{5}}\)