Q141 / 200 · Manipal (MET) 2012 · Physics
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$\sqrt{8}$
- Correct answerB$\sqrt{2 / 17}$
- C$\sqrt{1 / 8}$
- D$\sqrt{32 / 17}$
Solution
Let one mole of each gas has same volume as $V$. When they are mixed, then density of mixture is
$\begin{aligned}
\rho_{\text {mixture }} & =\frac{\text { mass of } \mathrm{O}_2+\text { mass of } \mathrm{H}_2}{\text { volume of } \mathrm{O}_2+\text { volume of } \mathrm{H}_2} \\
& =\frac{32+2}{V+V}=\frac{34}{2 V}=\frac{17}{V}
\end{aligned}$
Also, $\rho_{\mathrm{H}_2}=\frac{2}{V}$
$\begin{aligned}
\text {Now, velocity } v & =\left(\frac{\gamma P}{\rho}\right)^{1 / 2} \text { or } v \propto \frac{1}{\sqrt{\rho}} \\
\frac{v_{\text {mixture }}}{v_{\mathrm{H}_2}} & =\sqrt{\left(\frac{\rho_{\mathrm{H}_2}}{\rho_{\text {mixture }}}\right)} \\
& =\sqrt{\left(\frac{2 / V}{17 / V}\right)}=\sqrt{\left(\frac{2}{17}\right)}
\end{aligned}$
Hence, the correct answer is option: 'B'.