The displacement amplitude of a sound wave has a more direct influence on the loudness of the sound than the pressure amplitude.
In a sound wave, the displacement amplitude refers to the maximum distance that particles in the medium (such as air molecules) move from their equilibrium position as the wave passes through. It represents the extent of the back-and-forth motion of the particles caused by the sound wave.
The pressure amplitude, on the other hand, refers to the maximum deviation of the pressure from the average atmospheric pressure caused by the sound wave. It represents the variation in the density or compression of the medium.
While both displacement and pressure are related in a sound wave, the displacement amplitude is a more direct measure of the physical displacement of the particles, which is more closely related to our perception of loudness. When the displacement amplitude of a sound wave is larger, it means that the particles are moving more vigorously, resulting in a higher perceived loudness. The pressure amplitude alone does not provide a direct indication of the physical displacement of particles and may not correlate as strongly with the perceived loudness.