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The wave won't push you along at the speed of sound; at any point on the wave from the wave's reference frame (the speed of sound) there is a net flow of particles heading the opposite direction, unless your amplitude gets so high that average particle velocity in some places starts to exceed the speed of sound, in which case you don't have a sound wave anymore I don't think.

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I agree about the particles moving in the waves frame, but what you are talking about is drag, I think. The pressure gradient still produces a net force on the object. How big it is compared with other forces, such as drag, I have no idea.

If you are talking about the gradient I think you are, any effect it has it can minimized to nearly nonexistent by increasing the wavelength.

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