Wave equation. Differential equation important in physics Spherical waves coming from a point source A solution to the 2D wave equation The (two-way) wave equation is a second-order linear partial differential equation for the description of waves or standing wave fields – as they occur in classical physics – such as mechanical waves (e.g. water waves, sound waves and seismic waves) or electromagnetic waves (including light waves). It arises in fields like acoustics, electromagnetism, and fluid dynamics. Single mechanical or electromagnetic waves propagating in a pre-defined direction can also be described with the first-order one-way wave equation, which is much easier to solve and also valid for inhomogeneous media. Introduction[edit] The (two-way) wave equation is a second-order partial differential equation describing waves, including traveling and standing waves; the latter can be considered as linear superpositions of waves traveling in opposite directions.
The scalar wave equation is In other words: Related pages. Linear & Second Order Wave Theory. Helmholtz equation. Examples. Transmission Line Theory. Telegrapher Equation. Acoustics.
Derivation of the Wave Equation. Wave equation, wikipedia. Spherical waves coming from a point source. The wave equation is an important second-order linear partial differential equation for the description of waves – as they occur in physics – such as sound waves, light waves and water 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.[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] Introduction[edit] where ∇2 is the (spatial) Laplacian and where c is a fixed constant. The equation alone does not specify a solution; a unique solution is usually obtained by setting a problem with further conditions, such as initial conditions, which prescribe the value and velocity of the wave.
Scalar wave equation in one space dimension[edit] . . Waves (physics) Waves. Equations of physics. Hyperbolic partial differential equations. Wave Mechanics. Laplacian Equations.