Apologies for any confusion caused. You are correct in stating that the amplitude in mechanical waves refers to the maximum value of the disturbance of particles from their mean position. However, it is important to note that waves themselves do not possess an amplitude.
In the context of a wave, such as a sound wave or water wave, the term "amplitude of the wave" refers to the maximum magnitude of the disturbance that the wave is capable of producing in the medium through which it propagates. It represents the maximum value of the wave's disturbance at any given point in space.
For example, in a water wave, the amplitude would represent the maximum height of the wave crest or the maximum depth of the wave trough from the undisturbed water level. In a sound wave, the amplitude would correspond to the maximum displacement of air particles from their equilibrium position as the wave passes through the medium.
So, when we refer to the "amplitude of the wave," we are essentially describing the maximum magnitude of the wave's disturbance or the maximum value that the wave reaches at any given point in space. The wave itself is characterized by its properties such as frequency, wavelength, and speed, while the amplitude describes the intensity or magnitude of the wave's disturbance.