Speed of sound in a gas and speed of a typical gas molecule Why is speed of sound in a gas  less than the average velocity of the gas molecules? Is there an intuitive way to explain this?
 A: I know the derivation of $v_\text{sound}=\sqrt{\frac{\gamma p}{\rho}}\ $ from macroscopic principles, but I've always thought that there must be a way of deriving it on a molecular level. And I've sometimes wondered about the question being asked here: not so much that $v_\text{sound}\ $ is less than $v_\text{rms}$, as that the two speeds are so close. What follows is speculative and hand-wavy, so please regard it as a possible jumping-off point for further investigation.
As I see it, the sound, perhaps generated by the moving cone of a loudspeaker, superimposes a small velocity on the fast random motion of the molecules. This superimposed velocity is likely to be passed on to other molecules in collisions. But the speed of propagation is almost entirely determined by the random thermal speed of the molecules (since the superimposed 'sonic' velocity is very small by comparison). This accounts for why $v_\text{sound
}\ $ should be close to $v_\text{rms}\ $.
But when one molecule carrying the sonic velocity hits another molecule it has a tendency to pass on that velocity to the molecule it hits, the second molecule is unlikely to leave the collision in the same direction that the first molecule was travelling in, so you'd expect that over a distance, the sound would travel more slowly than the rms speed of the molecules, because, on a microscopic scale, it's not travelling in a straight line.
A: Gas molecules moving with an average speed and sound propagation are two different things. Something you have to keep in mind is that sound is not transmitted by the net motion of particles. Sound is transmitted via pressure waves (or you can just say sound is pressure waves). Furthermore, that the gas molecules have an average speed does not mean that the molecules have a net movement in any direction.
So I would say there is not really a direct relationship. To see this, think about solids. The molecules in a solid are pretty much confined to a lattice-like structure, but the speed of sound in solids tend to be much greater than the speed of sound in fluids.
