what is the relationship between the movement of the wave and the movement of the particles o the mudium ?

Question

what is the relationship between the movement of the wave and the movement of the particles o the mudium ?

Answer 1

If you're referring to a surface wave, see ref. 1 and use "track on". Use the step-by-step option to clarify particle motion and try different phases. Also see ref. 2.
If not a surface wave, you could be talking about a sound wave. In that case, the air molecules move forward and backward along the direction of wave motion. This is called a longitudinal wave. See ref. 2.
In general the relation between wave and particle motion is that wave motion can cover large distances while particle motion is restricted to a small path that is repeated; there is no long-term or steady motion component. The particles move in a plane that contains the propagation direction of the wave.