Many problems in science and engineering are governed by hyperbolic partial differential equations. However, solving these problems are not always easy and proper care should be taken in developing suitable algorithms. Wave equations are one of the most important hyperbolic equations which occur in many realistic situations when some wave motions are involved. Some of the applications include but are not restricted to supersonic flow, vibration of strings and membranes, electromagnetic wave simulation, oceanography, and acoustics design. This study aims to develop an efficient algorithm to solve the problem of wave propagation as a function of space and time through solving both homogeneous and non-homogenous wave equations. There are three different numerical algorithms namely the explicit, implicit, and hybrid schemes that had been developed based on finite difference methods (FDM). A generalized computer program in C++ is developed to solve the wave equations using these three different schemes. The computed results had been validated against analytical solutions for homogeneous wave equations. Excellent agreement has been found both in the transient behavior as well as in the spatial distribution of the dependent variable. The simulation software of this study has the capability to test any type of boundary and initial conditions, different schemes, and solve heterogeneous and homogeneous equations.