One of the fundamental problems of physics is the wave, which involves partial differential equations. Among the methods used in the solution of the one-dimensional wave equation, the methods of separating variables and finite differences stand out. For this, a description of the fundamental concepts about waves with emphasis in mechanical waves was realized. For the one-dimensional wave equation, three distinct demonstrations were made to obtain it, which is a second-order differential equation dependent on a temporal and a spatial variable. Through the methods of separating variables and finite differences, we found their analytical and numerical solutions, respectively. Comparisons were made between them in two problems, and a problem was presented for the stability analysis of the numerical method. The graphs showed a satisfactory fit between the analytical and numerical solutions, making an alternative the use of the numerical method, especially to solve problems that do not exist exact solution by the analytical method.
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