The type of wave that displaces the particles of the medium parallel to the direction in which it travels is a longitudinal wave.

Here's a breakdown:

* Longitudinal waves: The particles of the medium vibrate back and forth in the same direction as the wave travels. Think of a slinky stretched out and then pushed, creating a compression that travels along the slinky. Sound waves are a classic example of longitudinal waves.

* Transverse waves: The particles of the medium vibrate perpendicular to the direction the wave travels. Imagine shaking a rope up and down, creating a wave that moves horizontally. Light waves are an example of transverse waves.