Wave equation is a very important equation in applied mathematics. This equation is used to simulate large destructive waves in fjord, lake, or the ocean generated by slides, earthquakes, subsea volcanoes, meteorites. It has analytical solution but it is time consuming. Therefore one needs to use numerical methods for solving this equation. For this we investigate finite difference method and present explicit upwind difference scheme for one dimensional wave equation, central difference scheme for second order wave equation. We implement the numerical scheme by computer programming for initial boundary value problem and verify the qualitative behavior of the numerical solution of the wave equation.