Sound waves, which are longitudinal waves, can be modeled as the displacement amplitude varying as a function of the spatial and temporal coordinates. As a column of the medium is displaced, its successive columns are also displaced. As the successive displacements differ relatively, a pressure difference with the surrounding pressure is created. The gauge pressure varies across the medium.
The pressure fluctuation depends on the difference in displacements between the successive points in the medium. A relationship between the instantaneous displacement of a particle in the medium and the gauge pressure can be obtained via the material's bulk modulus.
At points of compression, the pressure is the most positive because the medium's particles aggregate. At points of rarefaction, the particles are the farthest from each other, and the pressure is the most negative. In between, where the particles have maximum displacement, the pressure is zero.
Waves of shorter wavelengths have greater pressure amplitudes, and vice versa.
