In the context of waves, the motion of particles is often involved in creating and propagating waves. However, it's important to distinguish between the motion of individual particles and the overall motion of a wave.
In a mechanical wave, such as waves on the surface of water or sound waves in air, the particles of the medium oscillate or vibrate around their equilibrium positions. As one particle is displaced from its equilibrium position, it exerts a force on its neighboring particles, causing them to also move from their equilibrium positions. This transfer of energy from particle to particle creates a wave-like motion that propagates through the medium.
However, it's worth noting that the particles themselves do not necessarily move along with the wave. For example, in an ocean wave, individual water molecules mostly move in a circular motion as the wave passes by, rather than being transported along with the wave in a particular direction.
In the case of electromagnetic waves, such as light, the wave is not dependent on the motion of particles in a medium. Instead, electromagnetic waves consist of oscillating electric and magnetic fields that propagate through space. In this case, the wave is not created by the motion of particles, but rather by the interaction of electric and magnetic fields.
So, while the motion of particles can be involved in the creation and propagation of waves, waves themselves can exist and propagate even in the absence of particles, as is the case with electromagnetic waves.