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$υ_{1} and υ_{2}$ are the velocities of sound at the same temperature in two monoatomic gases of densities $ρ_{1} and ρ_{2}$ respectively. If $\frac{ρ_{1}}{ρ_{2}} = \frac{1}{4}$ then the ratio of the velocities $υ_{1} and υ_{2}$ is

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1:4

1 :2

4:1

2:1

answer is C.

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Detailed Solution

Applying $C = \sqrt{\frac{γp}{ρ}}$

$C \propto \sqrt{\frac{1}{ρ}}$

$\Rightarrow \frac{C_{1}}{C_{2}} = \sqrt{\frac{ρ_{2}}{ρ_{1}}} = \sqrt{4} = 2$

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