The type of mechanical wave where particles in the medium move back and forth in the direction of the wave's motion is called a longitudinal wave.

Here's why:

* Longitudinal Waves: In these waves, the particles oscillate parallel to the direction the wave travels. Think of a slinky: when you push one end, the compression travels along the slinky, causing the coils to move back and forth in the same direction as the wave. Examples include sound waves and seismic P-waves.

* Transverse Waves: In these waves, the particles oscillate perpendicular to the direction the wave travels. Imagine a rope tied to a wall: if you shake it up and down, the wave travels along the rope, but the rope's individual parts move up and down, perpendicular to the wave's direction. Examples include light waves and seismic S-waves.