What term describes the maximum displacement of particles of the medium from their mean positions in waves?

The term that describes the maximum displacement of particles of the medium from their mean positions in waves is amplitude. Amplitude measures how far a wave's particles move from their equilibrium position during oscillation. In the context of transverse waves, for example, it represents the height of the wave crest or the depth of the trough relative to the mean position.

Understanding amplitude is crucial as it relates to energy transfer in waves; larger amplitudes typically indicate a greater amount of energy carried by the wave. This concept is vital in fields such as physics and engineering, where the behavior of waves needs to be quantified and applied. Other terms like frequency, wavelength, and energy each define different characteristics of waves and do not directly refer to the maximum displacement of particles.