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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
Waves
Solution:
Let $V$ be the volume of each gas. Then
Density mixture, $ \rho_{\text{mix}}=\frac{\text { total mass }}{\text { total volume }} $
$=\frac{V \rho_{ H _{2}}+V \rho_{ O _{2}}}{V+V}=\frac{V \rho_{ H _{2}}+V\left(16 \rho_{ H _{2}}\right)}{2 V}=\frac{17}{2} \rho_{ H _{2}}$
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}}$