Question

Oxygen is 16 times heavier than hydrogen. Equal volumes of hydrogen and oxygen are mixed. The ratio of speed of sound in the mixture to that in hydrogen is

• A. $\sqrt{8}$
• B. $\sqrt{2/17}$
• C. $\sqrt{1/8}$
• D. $\sqrt{32/17}$

Answer 1

Answer: (B)

Let $V$ be the volume of each gas. Then
Density mixture, ${\rho }_{\text{mix}}=\frac{\text{ total mass }}{\text{ total volume }}$
$=\frac{V{\rho }_{H_2}+V{\rho }_{O_2}}{V+V}=\frac{V{\rho }_{H_2}+V\left(16{\rho }_{H_2}\right)}{2V}=\frac{17}{2}{\rho }_{H_2}$
As $v=\sqrt{\frac{\gamma P}{\rho }}\text{ or }v\propto \frac{1}{\sqrt{\rho }}$
$\therefore \frac{v_{\text{mix}}}{v_{H_2}}=\sqrt{\frac{{\rho }_{H_2}}{{\rho }_{\text{mix}}}}=\sqrt{\frac{2}{17}}$