Wave Processes and their Visualization

<jats:p>The article investigates a mathematical model of two-dimensional wave processes based. The main properties of wave functions as functions of several variables are considered, and their differential characteristics, including partial derivatives and the Laplace operator, are analyzed. It is shown that the given harmonic wave functions are particular solutions of the Helmholtz equation, and the possibility of representing a two-dimensional wave as a superposition of one-dimensional harmonic components is demonstrated. Special attention is paid to the computer visualization of wave processes using the GeoGebra environment, which provides a clear interpretation of analytical results and contributes to the development of an intuitive understanding of the spatial structure of wave fields. The obtained results have educational and methodological value and can be used in secondary school and university courses in mathematics and mathematical physics.</jats:p>