The amplitude of a wave is a measure of its maximum displacement from its rest position. This displacement is directly related to the energy carried by the wave; larger amplitudes indicate higher energy. In the context of mechanical waves, such as sound waves, greater amplitude results in louder sounds, while for electromagnetic waves, larger amplitudes correspond to brighter light. Thus, when discussing amplitude in relation to a wave, the relationship with energy is critical, making it clear that it is the correct answer.
In contrast, frequency refers to how many cycles of the wave occur per second, speed is the rate at which the wave travels through a medium, and wavelength measures the distance between consecutive corresponding points on the wave. Each of these characteristics describes different aspects of a wave and does not relate to the amplitude's indication of energy.