DERIVATION OF CONVECTIVE KIRCHHOFF’S FORMULA FOR FAR-FIELD PROPAGATION OF SOUND

摘要

The Kirchhoff’s formula is a useful formula for the wave propagation. The wave property at a desiredrnobserver position can be obtained through a surface integration for closed surface surrounding the source,rnso-called the Kirchhoff’s surface. The classical Kirchhoff’s formula is based on the wave equation forrnstationary medium. This paper describes a Kirchhoff’s formula for the convective wave equation, whichrnincludes a moving medium effect. The generalized function theory is used for derivation of generalizedrnconvective wave equation. The integral form solution, the Kirchhoff’s formula, is obtained using arnconvective Green’s function for an arbitrarily moving surface. The derived formula has similar form withrnthe classical Kirchhoff’s formula but an additional term appears due to a moving medium effect. Forrnconvenience, manipulation is applied to the additional term and a final form like the classical formula isrnobtained.