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Q.
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
ManipalManipal 2012
Solution:
Let one mole of each gas has same volume as $V$.
When they are mixed, then density of mixture is
$\rho_{\text {mixture }}=\frac{\text { mass of } O _{2}+\text { mass of } H _{2}}{\text { volume of } O _{2}+\text { volume of } H _{2}}$
$=\frac{32+2}{V+V}=\frac{34}{2 V}=\frac{17}{V}$
Also, $\rho_{ H _{2}}=\frac{2}{V}$
Now, velocity $v=\left(\frac{\gamma P}{\rho}\right)^{1 / 2}$
or $v \propto \frac{1}{\sqrt{\rho}}$
$\frac{v_{\text {mixture }}}{v_{ H _{2}}}=\sqrt{\left(\frac{\rho_{ H _{2}}}{\rho_{\text {mixture }}}\right)}$
$=\sqrt{\left(\frac{2 / V}{17 / V}\right)}=\sqrt{\left(\frac{2}{17}\right)}$