Question

The ratio of the speed of sound in nitrogen gas to that in helium gas at 300 K is

• A. $\sqrt{\frac{2}{5}}$
• B. $\sqrt{\frac{2}{7}}$
• C. $\frac{\sqrt{3}}{5}$
• D. $\frac{\sqrt{6}}{5}$

Answer 1

The correct option is C $\frac{\sqrt{3}}{5}$

Speed of sound wave,
$c=\sqrt{\frac{\gamma RT}{M}}$
$\frac{c_{N_2}}{c_{He}}=\sqrt{\frac{{\gamma }_{N_2}}{{\gamma }_{He}}\times \frac{M_{He}}{M_{N_2}}}=\sqrt{\frac{7}{5}\times \frac{3}{5}\times \frac{4}{28}}$
$\frac{c_{N_2}}{c_{He}}=\frac{\sqrt{3}}{5}$