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The wave equation is a second-order linear partial differential equation for the description of waves or standing wave fields 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.
The phase velocity is the rate at which the phase of the wave propagates in space. The group velocity is the rate at which the wave envelope, i.e. the changes in amplitude, propagates. The wave envelope is the profile of the wave amplitudes; all transverse displacements are bound by the envelope profile.
The wave equation describing a standing wave field in one dimension (position ) is p x x − 1 c 2 p t t = 0 , {\displaystyle p_{xx}-{\frac {1}{c^{2}}}p_{tt}=0,} where p {\displaystyle p} is the acoustic pressure (the local deviation from the ambient pressure) and c {\displaystyle c} the speed of sound , using subscript notation for the partial ...
Alternatively, given suitable Lagrangian or Hamiltonian densities and using the principle of stationary action, the wave equations can be obtained also. For example, Maxwell's equations can be used to derive inhomogeneous electromagnetic wave equations, and from the Einstein field equations one can derive equations for gravitational waves.
The equations themselves are called "wave equations" or "field equations", because they have the mathematical form of a wave equation or are generated from a Lagrangian density and the field-theoretic Euler–Lagrange equations (see classical field theory for background).
In fluid dynamics, the Davey–Stewartson equation ... It is a system of partial differential equations for a complex (wave-amplitude) field and a real ...
A one-way wave equation is a first-order partial differential equation describing one wave traveling in a direction defined by the vector wave velocity. It contrasts with the second-order two-way wave equation describing a standing wavefield resulting from superposition of two waves in opposite directions (using the squared scalar wave velocity).
An acoustic wave is a mechanical wave that transmits energy through the movements of atoms and molecules. Acoustic waves transmit through fluids in a longitudinal manner (movement of particles are parallel to the direction of propagation of the wave); in contrast to electromagnetic waves that transmit in transverse manner (movement of particles at a right angle to the direction of propagation ...