Archives of Acoustics, 31, 4(S), pp. 115-121, 2006

Sound wave propagation problems new perturbation methodology

Jerzy Skrzypczyk
Silesian University of Technology, Faculty of Civil Engineering, Akademicka 5, 44-100 Gliwice
Poland

A. Winkler-Skalna
Silesian University of Technology, Faculty of Civil Engineering, Akademicka 5, 44-100 Gliwice
Poland

The aim of the paper is to present applications of the new algebraic system theory in acoustic
problems. Elements of new types of perturbed ordinary and partial differential equations
are discussed. The formulation is applied to the analysis of perturbed wave problems with
perturbations in parameters as well as in initial and boundary conditions. Classical perturbation
acoustic problems described by differential equations can be solved in the modified
algebraic system as easy as usual. Any additional analytical transformations are not required.
A novel 2D ray-tracing model of detailed representation of the indoor/outdoor environment
is presented. Perturbation ray tracing method is a technique based on geometrical optics with
perturbation in parameters which can be an easily applied approximate method for estimating
perturbation problems in acoustics. The developed algorithms use the new perturbation
methodology where the perturbed images are used to produce 2D-field of illumination zones.
It can be easy considered how perturbations (small) of nominal parameter values can change
solutions of the considered problems.
Keywords: perturbation numbers, perturbed DE, ray tracing.
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