Awave is traveling through a medium ad it travels it displaces particles of matter in the same direction as the wave is traveling this type of wave is a

Longitudinal wave

Explanation:

Longitudinal wave: this wave produces vibrations in the direction it moves, that is, it pushes the particles in the medium towards their direction of propagation.

Unlike another type of wave that is the transverse wave, which produces  vibration in a direction perpendicular to its direction of propagation.

So the wave mentioned in the statement is a longitudinal wave because the displacement of the particles is in the direction of the wave.

An example of this type of wave are sound waves, which are transmitted by vibrations in the particles of the medium (like air) in their direction of the movement of the wave.