Which type of wave moves a medium back and forth along the path of the wave?

The correct answer is a longitudinal wave. Longitudinal waves are characterized by the movement of the medium's particles back and forth along the same direction in which the wave travels. This means that as the wave travels, it compresses and retracts the particles of the medium, creating areas of compression and rarefaction.

For instance, in sound waves, which are a common example of longitudinal waves, the air molecules vibrate parallel to the direction of the wave propagation, leading to the transportation of sound energy through the air. Understanding this fundamental characteristic helps to differentiate longitudinal waves from other types, such as transverse waves, where the medium moves perpendicular to the wave direction, creating crests and troughs instead of compressions and rarefactions.