The wave equation is a mathematical formula that describes how waves propagate through different mediums, such as air, water, or solids. It is commonly expressed in the form of a partial differential equation, which relates the second derivative of a wave function to its spatial and temporal changes. This equation is fundamental in fields like physics and engineering, helping to analyze phenomena such as sound, light, and seismic waves. In its simplest form, the wave equation can be written as ∂²u/∂t² = c²∂²u/∂x², where u represents the wave function, t is time, x is position, and c is the speed of the wave in the medium. Solutions to the wave equation provide insights into wave behavior, including reflection, refraction, and interference, making it essential for understanding various physical systems.