Here's the breakdown:

* Transverse wave: The particles of the medium oscillate perpendicular to the direction the wave travels. Think of a ripple in water or a wave on a string.

* Longitudinal wave: The particles of the medium oscillate parallel to the direction the wave travels. Sound waves are a good example of this.

Key point: Mechanical waves require a medium to travel through. This means they can't travel through a vacuum like light waves.