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

The correct option is B $\sqrt{2/17}$

Let one mole of each gas has same volume as V. When they are mixed, then density of mixture is
${\rho }_{mixture}=\frac{massof{O}_2+massof{H}_2}{volumeof{O}_2+volumeof{H}_2}$
$=\frac{32+2}{V+V}=\frac{34}{2V}=\frac{17}{V}$
Also, ${\rho }_{H_2}=\frac{2}{V}$
Now, velocity $v={\left(\frac{\gamma P}{\rho }\right)}^{1/2}$ or $v\propto \frac{1}{\sqrt{p}}$
$\frac{v_{mixture}}{v_{H_2}}=\sqrt{\left(\frac{{\rho }_{H_2}}{{\rho }_{mixture}}\right)}$
$=\sqrt{\left(\frac{2/V}{17/V}\right)}=\sqrt{\left(\frac{2}{17}\right)}$