A brief tutorial on the fast field program (FFP) as applied to sound propagation in the air

The Fast Field Program (FFP), a computational technique originally developed for predicting acoustic wave propagation in the sea, has proved useful for calculating sound propagation in the air above the ground. The procedure involves the Hankel transformation of the Helmholtz equation in circular cylindrical co-ordinates, and the integration of the resulting ordinary differential equation by analogy with electrical transmission lines. Variation of the sound speed in the vertical co-ordinate is represented by horizontal stratification of the air into discrete layers, each with a different sound speed homogeneous and isotropic within the layer. The heights of source and detection points can be arbitrarily assigned, as can the ground impedance. It is assumed that there is no azimuthal variation of sound pressure and that there is no range dependence of ground impedance or atmospheric parameters. The computation yields the sound pressure, at a given detector height, for a continuous range of source to detector radii. This tutorial paper gives a detailed account of the theory of the FFP, describes the current implementation in terms of discrete variables, and references the original sources of the technique.