Physics - Sound Wave Question with Solution | TestHub

The speed of sound in a gas is given by $v=\sqrt{\frac{\gamma RT}{M}}$.

For helium, ${\gamma }_{He}=\frac{5}{3}$ and $M_{He}=4$.

For nitrogen, ${\gamma }_{N_2}=\frac{7}{5}$ and $M_{N_2}=28$.

The ratio of the speed of sound in helium to that in nitrogen at the same temperature $T$ is:

$\frac{v_{He}}{v_{N_2}}=\sqrt{\frac{{\gamma }_{He}}{{\gamma }_{N_2}}\times \frac{M_{N_2}}{M_{He}}}$

Substituting the given values:

$\frac{v_{He}}{v_{N_2}}=\sqrt{\frac{5/3}{7/5}\times \frac{28}{4}}$

$\frac{v_{He}}{v_{N_2}}=\sqrt{\frac{25}{21}\times 7}=\sqrt{\frac{25}{3}}=\frac{5}{\sqrt{3}}$

Answer: $\frac{5}{\sqrt{3}}$