A plane wave (or plane parallel wave) is a theoretical wave such that the motions/changes occurring are the same across an entire mathematical plane, and the wave is traveling perpendicular to the plane. This is mathematically simpler than waves diverging from something, e.g., as expanding spheres, but a sub-region consisting of a small fraction of such an expanding sphere approximates a plane, and as such a wave progresses, using a plane wave as an approximation of the wave becomes more and more useful. Thus, a wave far from its source is often modeled as a plane wave to generalize the model and simplify the math. This is analogous to the "plane-parallel atmosphere" simplified model of atmospheres
Such a wave (if longitudinal) also approximates a wave within a cylindrical musical wind instrument such as a flute or organ pipe, one complicating factor being the effect of friction between the medium (air) and the surrounding inner pipe surface.