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.



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.

  • $\begingroup$ The most 'classical' application is a vibrating string (like a guitar string, or a piano string). The 1D wave equation almost perfectly describes the shape and frequency of standing waves on a stretched string (if it's thin enough). Also, if you've read the Wikipedia page, you were bound to see a lot of applications $\endgroup$ – Yuriy S Apr 27 '16 at 11:49

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.

  • $\begingroup$ Schrodinger is not a wave equation. You are confusing the OP. Wave equation is hyperbolic, while Schrodinger is parabolic. $\endgroup$ – Yuriy S Apr 27 '16 at 11:39
  • $\begingroup$ Hmm, clearly I'm abusing the language of the domain then. But you're right, the Schrodinger equation is a diffusion equation. $\endgroup$ – Mathematician 42 Apr 27 '16 at 12:23
  • $\begingroup$ Schrödinger's equation is dispersive equation. $\endgroup$ – Julián Aguirre Apr 28 '16 at 13:47

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