Wind, sound & the net displacement of air As I understand it, sound is a pressure wave that propagates through air via (localised) successive compressions and rarefactions of the air. The compressions and rarefactions of the air cause the molecules of air to oscillate about their equilibrium positions. The important point here being that there is no net displacement of air molecules on average, since the air molecules interact with their nearest neighbours during the compressions and rarefactions exerting opposing forces on each other causing their aforementioned oscillations about their equilibrium positions.
Wind, on the other hand, is caused by pressure gradients causing an (on average) net displacement of air from high pressure regions to low pressure ones.
My question is, Why is there no net displacement of air by sound (when it seems that the compressions and rarefactions cause localised pressure gradients), but there is in the case of wind?
 A: It is because the wind has an overall sign to the pressure gradient, whereas in pressure waves, the sign is both positive and negative, so cancels out.  It is true that the sound is propagating in a given direction, and nonlinear effects will indeed displace air in that direction, but in the case of a linear (i.e., very low amplitude) sound wave, there is complete symmetry between the regions that have a positive pressure gradient and regions that have a negative pressure gradient, and those regions constantly swap with each other, so the net displacement wouldn't know which way to point.
A: If a rope is on a train and we make waves propagate through the rope by shaking the end up and down, will it go faster than the train and get there first? The train is like wind and the waves are like sound. The waves move relative to the train but the rope doesnt. Sound waves move through air but at any point in the air, the air there will fluctuate up and down in pressure and not move overall due to sound. Waves through air moving not air moving.
