A wave equation is a mathematical formula that describes how waves propagate through different mediums, such as air, water, or solids. It typically relates the displacement of the wave to time and space, allowing us to understand how waves move and change over time. The most common form is the linear wave equation, which applies to many types of waves, including sound and light. Wave equations are essential in various fields, including physics, engineering, and even finance. They help scientists and engineers predict behaviors of waves, such as sound waves, electromagnetic waves, and ocean waves. Understanding these equations is crucial for applications like acoustics, optics, and seismology.