The type of wave that pushes particles together and then 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.

* Transverse waves, on the other hand, move particles perpendicular to the direction of wave propagation.

Examples of longitudinal waves:

* Sound waves: Sound travels through air, water, or solids by compressing and expanding the molecules of the medium.

* Seismic waves (P-waves): These waves are responsible for the initial shaking during earthquakes. They compress and expand the ground as they travel.

Key takeaway: Longitudinal waves are the type of waves that push particles together (compression) and then spread them apart (rarefaction) as they travel.