Modeling the propagation of a modulated ultrasonic wave in a nonlinear medium

The present article discusses the possibilities of transmitting and focusing a modulated ultrasonic wave in a nonlinear medium. From a more concrete perspective, the analyzed problem consists in the propagation of an ultrasonic wave in such a medium. The examined subject is connected with mathematical tools related to the Westervelt equation, which describes and models the propagation of ultrasonic waves in the context outlined herein, enabling us to simulate the propagation and focusing of ultrasonic waves in various media. The paper characterizes the Westervelt equation in detail and introduces the mathematical tools that facilitate the numerical solution of the problem. In this context, the first chapter describes the individual parts of the equation, presenting a numerical instrument based on the pseudospectral Fourier collocation method to allow its solution. The second section of the text defines the input parameters and properties of the applied medium for the modeling and propagation of an ultrasonic wave and refers to two types of amplitude modulation in which we investigated the influence on the propagation and distortion of the transmitted sound beam. The final chapter then summarizes the results and proposes a comparison of the simulations performed. To solve the discussed problem, we used the k-wave toolbox for Matlab.