The molecular speed of gas formula, $$v=\sqrt{\frac{3RT}{M}}$$, is applicable to air, which is a mixture of gases, primarily nitrogen and oxygen. The molecular weight of air is approximately 28.96 g/mole, calculated using the contributions of N2, O2, and Ar. The computed root mean square (RMS) velocity of air correlates with the speed of sound, where the speed of sound $$v_s$$ is related to the RMS molecular speed $$v_m$$ by the equation $$\frac{v_s}{v_m}=\sqrt{\frac{\gamma}{3}}$$, with $$\gamma$$ being 7/5 for diatomic gases. This relationship confirms that air can be modeled as a diatomic ideal gas for accurate results.
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For a given gas, the two are proportional.Baluncore said:I believe the computed RMS velocity gives you the speed of sound.
The article above goes on to provide an explanation for the relationship.https://physics.stackexchange.com/questions/78879/simple-explanation-of-relation-between-speed-of-sound-and-r-m-s-speed said:In an ideal gas, the speed of sound ##v_s## is related to the r.m.s. molecular speed ##v_m## by $$\frac{v_s}{v_m}=\sqrt{\frac{\gamma}{3}}$$where ##\gamma## = ##C_p/C_v## = 7/5 for a diatomic gas.