Mechanical waves are classified based on the direction of particle vibration relative to the direction of wave propagation. This leads to two main categories:

* Transverse waves: Particles vibrate perpendicular to the direction the wave travels. Examples include light waves, ripples in water, and waves on a string.

* Longitudinal waves: Particles vibrate parallel to the direction the wave travels. Examples include sound waves and seismic P-waves.

So, the direction of particle vibration is the key characteristic used to classify mechanical waves.