An Energetic Approach for the Simulation of Diffraction within Ray Tracing Based on the Uncertainty Relation

Abstract

In room acoustics as well as in noise immission prognosis, ray tracing methods are efficient and widely used. Nevertheless, as is well recognised, these energetic methods assuming incoherent superposition fail when diffraction becomes important. The aim is to solve this main deficiency, but the energetic model shall be retained. However, since random emitted particles never pass edges exactly, analytical edge diffraction approaches may not be applied. These and other general problems of combining diffractions with the numerical methods of geometrical room acoustics are discussed in the first part of the paper. To introduce diffraction but preserve the algorithmic advantage of ray tracing, the author had proposed a sound particle diffraction model based on Heisenbergs uncertainty relation (UR) introducing the concept of a 'diffraction angle probability' and an 'edge diffraction strength' (the closer the by-pass-distance the stronger the diffraction effect'). This model, already presented in 1986, demonstrated very good agreements with the expected transfer functions of the basic reference cases of a half-infinite screen and a slit in far field. It has now for the first time been embedded in a full ray tracing program enabling also finite source and receiver distances. The results have also been compared with the exact wave-theoretical results of Svenssont's secondary edge source model. For most cases of the screen and the slit the agreements are very good (less than 1 dB). Also - not self evident - the reciprocity principle seems fulfilled. Exploiting the UR seems to be a useful approach not only for light - as has been published in the field of optical ray tracing - but also for sound. However, whether the method works also with higher order diffraction and with other structures has not yet been investigated for sound. A very difficult practical problem remains the explosion of computing time which may be solved by the re-unification -algorithm provided by Quantized Pyramidal Beam Tracing.