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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?

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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.

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    $\begingroup$ Ah ok. So is the point that the air molecules oscillate about their equilibrium points, instead of experiencing a net displacement, because the local pressure gradients keep changing direction (changing between pointing "backwards" and "forwards")?! Am I correct in thinking that, in general, as far as mechanical waves are concerned, there is no net displacement of a medium due to a wave propagating through it due to the particles constituting the medium) experiencing a restoring force, causing them to oscillate about their equilibrium positions... $\endgroup$
    – Feyn_example
    Nov 30, 2016 at 21:41
  • $\begingroup$ ... (in the case of sound in air, it is the local pressure gradients resulting from the compression and rarefaction of the local region of air that act as a restoring force, causing the air molecules to oscillate about their equilibrium positions)?! $\endgroup$
    – Feyn_example
    Nov 30, 2016 at 21:42
  • $\begingroup$ As far as mechanical waves are concerned that statement is mostly correct; it fails for example in a limited sense when a water wave hits the shore (the molecules in water waves otherwise tend to follow nice circular trajectories, ending up right where they started after the wave passes) and perhaps it fails when the water wave "crests" as it approaches the shore (since the circular motion presumably breaks down in the crest). $\endgroup$
    – CR Drost
    Nov 30, 2016 at 22:06
  • $\begingroup$ @CRDrost Ok, but neglecting these issues, is what I wrote correct in terms of restoring forces (and particular, in the case of sound, is the restoring force the pressure gradient arising from a compression or a rarefaction $\endgroup$
    – Feyn_example
    Nov 30, 2016 at 22:15
  • $\begingroup$ Yes. You could probably get a good distance, physics wise, by defining "waves are phenomena which transport net momentum without transporting net mass" or so. In the case of air, you indeed have these localized layers of high and low density stacked on top of each other, and the restoring force which propagates the wave is indeed the bulk modulus of the air. It's all about air molecules wanting to go from these places where they're concentrated to the next-door places where they're not, which provides the spring force that, like in a big slinky, propagates the compression wave. $\endgroup$
    – CR Drost
    Nov 30, 2016 at 22:57
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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.

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