Question

The ratio of speed of sound in $N_2$ gas to that in helium gas at $300$ K is?

• A. $\sqrt{2/7}$
• B. $\sqrt{1/7}$
• C. $\frac{\sqrt{3}}{5}$
• D. $\sqrt{6/5}$

Answer 1

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

We know,

Speed of sound in a medium,

$v=\sqrt{\frac{\gamma RT}{M}}$

Where $\gamma =\frac{C_p}{C_v},M=$Molecular Weight.

$\text{Case 1}$

$v_{N_2}=\sqrt{\frac{7RT}{5\times 28}}=\frac{1}{2\sqrt{5}}\sqrt{RT}$

$\text{Case 2}$

$v_{He}=\sqrt{\frac{5RT}{3\times 4}}=\frac{\sqrt{5}}{2\sqrt{3}}\sqrt{RT}$

$\frac{v_{N_2}}{v_{He}}=\frac{1}{2\sqrt{5}}\times \frac{2\sqrt{3}}{\sqrt{5}}$

$\frac{v_{N_2}}{v_{He}}=\frac{\sqrt{3}}{5}$

Option $\text{C}$ is the correct answer.