Final answer:
Matter moves back and forth in the same direction as the wave in a longitudinal wave, such as sound waves, where the particles of the medium move parallel to the wave's direction.
Step-by-step explanation:
The type of wave in which matter moves back and forth in the same direction as the wave is known as a longitudinal wave. In these waves, the particles of the medium vibrate parallel to the direction of wave propagation. This is in contrast with transverse waves, where the particles move perpendicular to the direction of the wave motion.
Sound waves are a common example of longitudinal waves, where you can observe the particles of the medium, such as air, oscillating back and forth in the same direction as the sound is traveling. The concept of wavelength is also applicable to particles of matter, described by the de Broglie wavelength.