How does a sound wave’s amplitude affect its loudness?

In the study of acoustics, the amplitude of a sound wave—defined as the maximum displacement or magnitude of pressure fluctuation from equilibrium—is the primary factor that determines its loudness.312

When a sound source vibrates with greater amplitude, it displaces more of the surrounding medium, such as air, which increases the wave's sound intensity. Intensity represents the rate of energy transmission per unit area, and because amplitude determines this intensity, a higher amplitude results in a sound that is perceived by the human ear as louder.31

While amplitude is a physical property that can be measured objectively, loudness is the subjective auditory sensation produced by that intensity. The relationship between the two is significant: for example, plucking a guitar string harder increases the amplitude of the resulting wave, thereby creating a louder sound.451