The discussion centers on the applicability of the molecular speed of gas formula, $$v=\sqrt{\frac{3RT}{M}}$$, specifically in the context of air, which is a mixture of different gases. Participants explore whether this formula can be used for air and how it relates to the speed of sound.
Participants generally agree that the molecular speed formula can be applied to air, but there is some uncertainty regarding the implications of this application, particularly in relation to the speed of sound.
There are assumptions regarding the ideal gas behavior of air and the treatment of its molecular composition that may not be universally applicable. The relationship between RMS speed and speed of sound is also contingent on the specific heat ratio, which may vary.
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.