page_title: Wave equation
section_title: Wave equation in one space dimension
hierarchical_section_title: Wave equation / Wave equation in one space dimension
caption_attribution_description: Français&#160;: Portrait de Jean Le Rond d'Alembert (1717-1783)
context_page_description: The wave equation is an important second-order linear partial differential equation for the description of waves—as they occur in classical physics—such as mechanical waves or light waves. It arises in fields like acoustics, electromagnetics, and fluid dynamics.
  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. In 1746, d’Alembert discovered the one-dimensional wave equation, and within ten years Euler discovered the three-dimensional wave equation.
context_section_description: The wave equation in one space dimension can be written as follows:
  .
  This equation is typically described as having only one space dimension x, because the only other independent variable is the time t.  Nevertheless, the dependent variable u may represent a second space dimension, if, for example, the displacement u takes place in y-direction, as in the case of a string that is located in the x–y plane.
caption: French scientist Jean-Baptiste le Rond d'Alembert (b. 1717) discovered the wave equation in one space dimension.[6]
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