I've recently started to take interest in PDEs and how to solve them, and I'm wondering a bit about real life applications of the wave equation. So far I haven't found anything about practical applications, but on Wikipedia it says that the wave equation is an important PDE that arises in fields like acoustics, electromagnetics and fluid dynamics. Since I know how to solve it I'd like to know how to apply it to something.
Thanks!
Edit:
Maybe I should clarify something. I know about areas where the wave equation is used and how a simple solution like sin(x-ct) + sin(x+ct) describes a standing wave. What I'm asking about is examples of real, practical situations where solving the wave equation with appropriate boundary conditions is necessary.
Best Answer
The entire field of quantum mechanics is based on the Schrödinger equation which is a wave equation. Any other field that studies waves (like water waves in fluid dynamics or acoustics, signal theory, $\dots$) needs wave equations.