Physics - Sound Wave Question with Solution | TestHub

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 $P=\frac{\rho RT}{M}$ by using the ideal gas equation, the speed of sound can be written as $c=\sqrt{\frac{\gamma RT}{M}}$. 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: $\frac{c_{\mathrm{He}}}{c_{{\mathrm{N}}_2}}=\sqrt{\frac{\frac{5}{3}}{\frac{7}{5}}\times \frac{28}{\sqrt{3}}}=\frac{5}{\sqrt{5}}$