The ratio of the speed of sound in nitrogen gas to that in helium gas, at 300K is

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$\frac{\sqrt{5}}{3}$

$\sqrt{\frac{3}{5}}$

$\frac{3}{\sqrt{5}}$

$\frac{\sqrt{3}}{5}$

answer is C.

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Detailed Solution

$C = \sqrt{\frac{r R T}{M}} \frac{C_{N_{2}}}{C_{H e}} = \sqrt{\frac{r_{N_{2}}}{r_{H e}} \times \frac{M_{H e}}{M_{N_{2}}}} = \sqrt{\frac{7}{5} \times \frac{3}{5} \times \frac{4}{28}} = \frac{\sqrt{3}}{5}$

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