Wave equation

Equations that describe waves as they occur in nature are called wave equations. Waves as they occur in rivers, lakes, and oceans are similar to those of sound and light. The problem of having to describe waves arises in fields like acoustics, electromagnetics, and fluid dynamics.

A pulse traveling through a string with fixed endpoints as modeled by the wave equation.

Spherical waves coming from a point source.

Historically, the problem of a vibrating string such as that of a musical instrument was studied by Jean le Rond d'Alembert, Leonhard Euler, Daniel Bernoulli, and Joseph-Louis Lagrange.^[1][2][3][4] In 1746, d’Alambert discovered the one-dimensional wave equation, and within ten years Euler discovered the three-dimensional wave equation.^[5]