The disturbance in the wave-motion is transferred from one particle to another of the medium due to repeated periodic oscillations of the particles about their mean fixed position (Equilibrium position).
The particles transfer the energy and momentum from one point to another without any actual transfer of the particles of the medium.
Since each and every particle of the medium receives disturbance a little later than its preceding particle, there is a regular phase difference between the particles.
The velocity of the wave and the velocity of the particle is not the same.
In any given medium the particle velocity varies during its vibration from its equilibrium position, whereas the velocity of the wave motion remains constant.
The velocity of the particle varies from zero to high, high at equilibrium and low at the peak (or trough).