The type of wave that pushes particles together and spreads them apart as it moves is a longitudinal wave.

Here's why:

* Longitudinal waves travel by compressing and expanding the medium they travel through. Think of a spring: if you push one end, you create a compression zone where the coils are closer together. This compression travels down the spring, followed by a rarefaction zone where the coils are further apart.

* Transverse waves travel by vibrating the medium perpendicular to the direction of the wave. Imagine shaking a rope up and down; the wave travels along the rope, but the rope itself moves up and down.

Examples of longitudinal waves:

* Sound waves: Sound travels through air by compressing and expanding the air molecules.

* Seismic P-waves: These waves are responsible for the "pushing" motion felt during an earthquake.

Let me know if you'd like more detail on any of these!