This project provides how the method of characteristics is applied to derivernthe fundamental solution of linear homogeneous wave equation and how shockrnwaves and shock solutions are formed by a discontinuous initial condition.rnMoreover, it provides how the solution of the linear non-homogeneous wavernequation is determined by combining the split equations, the homogeneousrnwave equation with non-zero initial data and the non-homogeneous wavernequation with zero initial data using method of characteristics.