An Analytically Derived Sound Particle Diffraction Model

Abstract

Ray tracing (RT) and mirror image source methods (MISM), widely used in room acoustics and in computing noise propagation, fail naturally when diffraction becomes important, especially in 'free field' (cities). Therefore, the goal is to extend these methods by an edge diffraction module, also for higher orders. Known analytical approaches for the diffraction at a wedge may be combined with the MISM but are inefficient. A direct combination with RT is not possible as random emitted particles never pass edges exactly. In 1986, the author proposed a sound particle diffraction model based on Heisenbergs uncertainty relation (UR) introducing the concept of a 'deflection angle probability density function' (DAPDF) ('the closer the by-pass distance at an edge, the stronger the deflection effect'). This heuristic model had given very good agreements with the expected transfer functions of the half-infinite screen and the slit but has the deficit of a missing analytical derivation. To overcome this, the author tried to derive such a DAPDF from the known Fresnel-Kirchhoff theory of diffraction at the half-infinite screen. This succeeded by assuming that the energy flow around the edge is simply cut off by a vertical shift of the screen: the 'hypothesis of the shifted screen'. But this solution was published only very briefly and only in German 1993. It is the aim of this paper to present here for the first time the full derivation. The agreements at the screen are very good but the model fails at a slit (two edges), hence, cannot be modularized as desired. Meanwhile (in 2006 and 2007) the UR-based diffraction model performed some new promising results. The deficiencies and chances of the two models are discussed.