In a longitudinal or transverse wave, what is the difference between the rest axis and the rest position? What do both represent?
I think these two terms are referring to essentially the same thing. Discussion below...
In the diagram below, the dashed line represents the rest position of the medium. This is where the medium would lie if undisturbed by the wave.
I must admit that I have not heard the term "rest axis" used in relation to this type of wave, but I assume it would refer to the same thing. Perhaps nothing more than a change of terminology? The rest axis is drawn to show the rest position of the medium?
In a longitudinal wave, a rest axis would apply only if we are considering a two-dimensional wave. There would be lines, perpendicular to the direction of travel of the wave, that would consist of particles that are undisturbed at a given moment. I don't see that the term would apply to a one-dimensional travelling longitudinal wave.