The wave equation, $\nabla^2p =\frac{1}{c^2}\,\frac{\partial^2 \,p^2}{\partial t^2}$

is a partial differential equation that describes the disturbance of a medium due to changes in pressure. The solution is often used to describe propagating waves in an acoustic environment. Such a scenario is solved using three main approaches: geometrical acoustics, waved-based techniques, and artificial methods. Here, we will discuss geometric and wave-based methods.
Geometrical acoustics is based on the assumption that sound travels as a particle in a ray instead of a wave. This only holds true when the model dimensions are much greater than the desired wavelengths. The underlying assumption omits any investigated of small room acoustics and low frequencies, leaving only large acoustic spaces. Wave phenomena, such as diffraction, are also unable to be modeled due to the limitations of geometrical acoustics. The most used computational algorithms in geometric techniques are ray-tracing and image-source method.
Wave-based techniques are a more accurate model that can describe wave propagation in a cavity (interior) or from a radiating body (exterior). Unlike geometric techniques, wave phenomena are modeled through numerical techniques including finite-difference time-domain (FDTD), finite element methods (FEM) and boundary element methods (BEM).