Sound wave propagation problems new perturbation methodology

Abstract

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.