Amplitude and displacement are related concepts but are distinct from each other in the context of waves.
Amplitude refers to the maximum magnitude or intensity of a wave. It represents the maximum distance that a wave's oscillation deviates from its equilibrium or rest position. In other words, it measures the extent of the wave's disturbance from its average or midpoint value. For example, in a transverse wave such as a water wave or a light wave, the amplitude is the maximum height or distance between the crest (peak) and the equilibrium position (the flat surface).
Displacement, on the other hand, refers to the position of a particle or point in a medium relative to its equilibrium position. It is the change in position of the particle from its original or reference position. Displacement can be positive or negative, depending on whether the particle is displaced above or below its equilibrium position. Displacement is typically measured from the wave's rest position to the current position of the particle.
To summarize, amplitude represents the maximum magnitude or intensity of a wave, while displacement refers to the change in position of a particle from its equilibrium position. Amplitude describes the wave's overall strength or magnitude, while displacement describes the position of a particle within the wave at a specific point in time.