${v_1}$ and ${v_2}$ are the velocities of sound at the same temperature in two monoatomic gases of densities ${\rho _1}$ and ${\rho _2}$ respectively. If $\frac{\rho _1}{\rho _2} = \frac{1}{4}$ then the ratio of velocities ${v_1}$ and ${v_2}$ will be
AIIMS 2002, Medium
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(c) At given temperature and pressure
$v \propto \frac{1}{{\sqrt \rho }}$
==>$\frac{{{v_1}}}{{{v_2}}} = \sqrt {\frac{{{\rho _2}}}{{{\rho _1}}}} = \sqrt {\frac{4}{1}} = 2:1$
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