Consider the sound wave travelling in ideal gases of He, $$CH_4$$, and $$CO_2$$. All the gases have the same ratio $$\dfrac{p}{\rho}$$, where P is the pressure and $$\rho$$ is the density. The ratio of the speed of sound through the gases $$v_{He} : v_{CH_4} : v_{CO_2}$$ is given by

$$v = \sqrt{\frac{\gamma P}{\rho}}$$

$$\gamma = 1 + \frac{2}{f}$$

$$\gamma_{\text{He}} = \frac{5}{3}$$

$$\gamma_{\text{CH}_4} = 1 + \frac{2}{6} = \frac{8}{6} = \frac{4}{3}$$

$$\gamma_{\text{CO}_2} = \frac{7}{5}$$

$$v_{\text{He}} : v_{\text{CH}_4} : v_{\text{CO}_2} = \sqrt{\gamma_{\text{He}}} : \sqrt{\gamma_{\text{CH}_4}} : \sqrt{\gamma_{\text{CO}_2}}$$

$$v_{\text{He}} : v_{\text{CH}_4} : v_{\text{CO}_2} = \sqrt{\frac{5}{3}} : \sqrt{\frac{4}{3}} : \sqrt{\frac{7}{5}}$$