Consider the sound wave travelling in ideal gases of $\mathrm{He}, \mathrm{CH}_4$, and $\mathrm{CO}_2$. All the gases have the same ratio $\frac{P}{\rho}$, where $P$ is the pressure and $\rho$ is the density. The ratio of the speed of sound through the gases $\mathrm{V}_{\mathrm{He}}: \mathrm{V}_{\mathrm{CH}_4}: \mathrm{V}_{\mathrm{CO}_2}$ is given by

The mean free path and the average speed of oxygen molecules at 300 K and 1 atm are $3 \times 10^{-7} \mathrm{~m}$ and $600 \mathrm{~m} / \mathrm{s}$, respectively. Find the frequency of its collisions.