Solutions of the Wave Equation

Waves are seen in many different applications, such as sound waves, electromagnetic waves, and ocean waves. They are typically modeled mathematically by sine and cosine functions. However, they are also modeled through partial differential equations, exhibiting aspects of position and time. This paper will be an exploration of solutions to one of these partial differential equations, called the wave equation, and will use various methods to solve boundary value problems. The Fourier method will be introduced and applied to the wave equation as well as Fourier series. These methods and applications will provide a better understanding of waves and the wave equation