The choice of using the amplitude as the highest positive displacement of a wave is based on convention and convenience. The amplitude represents the maximum extent to which a wave displaces from its equilibrium or mean position. It measures the magnitude or strength of the wave.
The convention of using the amplitude as the highest positive displacement is rooted in the concept of a sinusoidal wave, which is often used as a fundamental building block to analyze and describe various types of waves. In a sinusoidal wave, the amplitude represents the distance from the equilibrium position to either the crest (highest point) or trough (lowest point) of the wave.
By convention, the amplitude is typically defined as a positive value. This convention simplifies calculations and helps maintain consistency in mathematical representations of waves. It allows for straightforward calculations of quantities such as wave intensity, energy, and power, as these calculations often involve squaring the amplitude.
While it is possible to consider the negative displacement or the distance between the trough and the mean position as a measure of amplitude, it would introduce unnecessary complexity and potentially lead to confusion in wave analysis. Therefore, the convention of using the highest positive displacement as the amplitude is widely adopted to ensure clarity and consistency in the study and description of waves.