The type of wave that moves particles of the medium parallel to the direction in which the wave is traveling is called a longitudinal wave.

Here's why:

* Longitudinal waves involve the compression and rarefaction (expansion) of the medium.

* The particles oscillate back and forth *along* the direction the wave travels.

Examples of longitudinal waves:

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

* Seismic P-waves: These are the primary waves generated by earthquakes and travel through the Earth's interior by compressing and expanding the rock.

Let me know if you'd like to learn more about waves!