The amplitude of a wave is directly related to the height of its crests and the depth of its troughs. In a graphical representation of a wave, the amplitude is typically measured as the distance from the equilibrium position (the midpoint or baseline) to the highest point of the wave, which is the crest, or to the lowest point of the wave, which is the trough.
Mathematically, the amplitude (A) of a wave is defined as half the difference between the maximum and minimum values of the wave's displacement. It represents the maximum magnitude or strength of the wave.
For example, in a transverse wave traveling along a string, the amplitude corresponds to the maximum displacement of the string from its rest position. The crests of the wave represent the points where the string reaches its maximum positive displacement, while the troughs correspond to the points where it reaches its maximum negative displacement. The distance from the equilibrium position to either the crests or the troughs is equal to the amplitude of the wave.
Similarly, in a longitudinal wave, such as a sound wave traveling through air, the amplitude corresponds to the maximum compression or rarefaction of the air molecules. The regions of maximum compression correspond to the crests, while the regions of maximum rarefaction correspond to the troughs. The distance from the equilibrium position to either the crests or the troughs represents the amplitude of the wave.
In summary, the amplitude of a wave is directly related to the height of its crests and the depth of its troughs, representing the maximum displacement or magnitude of the wave from its equilibrium position.