Whats so amazing about the wave equation?

[toesockshoe]

From my understanding, all the wave equation says is the transverse acceleration of a particle on wave is equal to the the curvature of the of the wave at that point-particle times the propagation speed squared. Am i missing something?

 

[Orodruin]

The wave equation is not necessarily related to a mechanical wave. In itself it is an abstract concept with solutions which have many nice properties.

From a physical point of view, it turns out that the wave equation is successful in describing a large number of physical phenomena exactly or in a reasonable approximation (a mechanical wave on a string is only approximately described by the wave equation). It is therefore of large interest to study the wave equation and its solutions, as they have a large range of applications.