We know an elastic medium is necessary for the propagation of any kind of wave like sound. But air is not necessarily an elastic medium at all. For the compression and rarefaction which is extremely necessary for the wave to flow a dragging force is highly required to bring the particle to equilibrium. But in case of air the normal motion of the particles is a completely random one without any kind of equilibrium position at all. What causes the rare fraction and compression and causes the wave to flow in air? And again the potential between two gas molecules doesn't even obey hooke's law at all. Then how can i treat the displacement of a gas particle at time t and space x like y=asin(wt-kx)?
On an attempt to solve this problem I thought to expand the potential between gas molecules,whatever let it be,in a Taylor series with parabolic approximation but that also causes problem because the equilibrium position is not set.