Wave equations are mathematical descriptions that model how waves propagate through different mediums, such as air, water, or solids. They express the relationship between the wave's displacement, time, and spatial coordinates. Common examples include sound waves, light waves, and water waves, all of which can be analyzed using these equations. The general form of a wave equation is a second-order partial differential equation. It typically takes the shape of ∂²u/∂t² = c²∇²u, where u represents the wave function, c is the wave speed, and ∇² is the Laplacian operator. This framework helps scientists and engineers understand wave behavior in various applications.