The compressible NSE are rearranged into various forms of the inhomogeneous acoustic wave equation.
They consist of pressure and speed fluctuation as well as stress tensor and force terms.
Approximations are introduced to make the source terms independent of the acoustic variables.
In this way, linearized equations are derived which describe the propagation of the acoustic waves in a homogeneous, resting medium.
The Ffowcs Williams–Hawkings analogy is valid for aeroacoustic sources in relative motion with respect to a hard surface, as is the case in many technical applications for example in the automotive industry or in air travel.