ANALYSIS OF METHODS FOR MODELING SOUND PROPAGATION IN A WAVEGUIDE

Abstract

Computer study of processes of various nature requires the creation of a mathematical model of a natural experiment. The study process is greatly simplified when there is a visual component of such a process. The difficulty of developing a general mathematical model for the propagation of electromagnetic waves is associated with the dependence of the process on the medium. For example, in an aqueous environment, they are transmitted weaker than in an air environment, which makes their use in transmitting waves between objects in different environments inconvenient. Existing approaches to simulation of acoustic signal are considered in the work. Such methods include models of hydrodynamics in combination with Maxwell's equations, oscillating electrical circuits, methods for modeling the process of propagation and attenuation of sound under water, and others. The theoretical basis for constructing algorithms for modeling the propagation of acoustic oscillations in the marine environment is considered.

Mathematical and traditimic models of acoustic oscillations are based on preliminary tests and take into account the computer capabilities of technology. This constraint imposes additional conditions and complicates the mathematical model being created. The methods in question do not create mathematical models of the propagation and attenuation of sound signals, taking into account such user conditions as: variable speed of sound, geometry and bottom profile, surface state, medium temperature. Thus, there is a need to develop a methodology for modeling hydroacoustic signal components that describe the generation of signals and adapt to the task.

The analysis indicates the feasibility of using the methods of beam theory and the parabolic equation to describe a model for which the depth is variable.

Keywords: mathematical modeling, acoustic waves, wave equation, hydroacoustics, Helmholtz equation, beam method, normal modes, parabolic equation.