Definition

In a longitudinal wave, a compression is a region where the particles are squeezed close together and a rarefaction is a region where they are spread far apart, alternating along the direction of travel much like crests and troughs, except as squeezes and stretches instead of ups and downs, with the distance from one compression to the next equal to one wavelength. Compressions have higher particle density and pressure and rarefactions have lower density and pressure, and sound waves consist of these alternating regions moving through air, water, or solids. They mark the pressure maxima and minima of a longitudinal wave, $\Delta P(x,t) = \Delta P_{\max}\sin(kx - \omega t)$, where $\Delta P_{\max} = B k s_{\max}$ relates pressure amplitude to displacement amplitude through the bulk modulus $B$, the pressure wave leads the displacement wave by $90^\circ$ so particles sit at zero displacement at the center of a compression, and sound intensity is $I = \Delta P_{\max}^2/(2\rho v)$, scaling with the square of pressure amplitude.