rarefaction

Rarefaction refers to a region in a compressible medium where density and pressure are reduced below their surrounding values. In a propagating wave, such as a sound wave in air, the medium alternates between compressions (increased density and pressure) and rarefactions (decreased density and pressure). The concept is central to how waves transport energy through gases, liquids, and solids.

In acoustics, rarefaction corresponds to the low-pressure phase of a sound wave. For small amplitude, linear acoustics in an ideal gas, pressure p and density ρ are linked by p ≈ p0 + c2(ρ − ρ0), where c is the speed of sound. A rarefaction occurs when ρ decreases and p falls below ambient. The velocity of the particles is not the same as the wave’s propagation speed; particles oscillate around equilibrium while the wave travels at c.

In gas dynamics, a rarefaction wave is a self-similar solution to the Euler equations describing a smooth expansion from high to low pressure following a disturbance such as an opening of a valve or a piston retreat. Across the rarefaction fan, pressure, density, and temperature continuously decrease, and the fluid accelerates outward. Rarefaction waves contrast with shock waves, which involve abrupt increases in pressure and density.

Other contexts include seismology and fluid mechanics, where rarefactions are part of complex wavefields generated by impulsive sources. Understanding rarefaction helps explain how signals propagate, attenuate, and interact with boundaries in various media.