What is the closest definition of amplitude?

Amplitude refers specifically to the maximum distance that a wave moves away from its rest (or equilibrium) position. It quantifies the height of the wave's peaks and the depth of its troughs, which directly affects how loud a sound is perceived or how intense a light wave appears. This measurement is crucial because it indicates the energy of the wave: a wave with a larger amplitude carries more energy, whereas a wave with a smaller amplitude carries less energy.

While the other concepts mentioned, such as energy, speed, and frequency, are integral to understanding wave mechanics, they describe different aspects of wave behavior. For instance, energy relates to the amplitude but is not the definition itself. Similarly, speed and frequency are connected to how waves propagate and oscillate but do not describe the distance from the wave's rest position.