A pulse traveling through a string with fixed endpoints as modeled by the wave equation
Spherical waves coming from a point source
A solution to the 2D wave equation
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.
This article focus on two-way waves in classical physics. 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. Quantum physics uses an operator-based wave equation often as a relativistic wave equation.
The waveequation is a second-order linear partial differential equation for the description of waves or standing wave fields such as mechanical waves (e...
electromagnetic waveequation is a second-order partial differential equation that describes the propagation of electromagnetic waves through a medium...
physics, the acoustic waveequation is a second-order partial differential equation that governs the propagation of acoustic waves through a material medium...
where the wave amplitude appears smaller or even zero. Waves are often described by a waveequation (standing wave field of two opposite waves) or a one-way...
Schrödinger equation determines how wave functions evolve over time, and a wave function behaves qualitatively like other waves, such as water waves or waves on...
the waveequation, the diffusion equation, and the Schrödinger equation for a free particle. In optics, the Helmholtz equation is the waveequation for...
mechanics (RQM) and its applications to particle physics, relativistic waveequations predict the behavior of particles at high energies and velocities comparable...
speed of EM waves predicted by the waveequation coincided with the measured speed of light, Maxwell concluded that light itself is an EM wave. Maxwell's...
acoustic wave transmits in both longitudinal and transverse manners due to presence of shear moduli in such a state of matter. The acoustic waveequation describes...
In particle physics, the Dirac equation is a relativistic waveequation derived by British physicist Paul Dirac in 1928. In its free form, or including...
dynamics, a cnoidal wave is a nonlinear[disambiguation needed] and exact periodic wave solution of the Korteweg–de Vries equation. These solutions are...
}}} Taking the divergence of seismic waveequation in homogeneous media, instead of the curl, yields a waveequation describing propagation of the quantity...
one-dimensional waveequation, and within ten years Euler discovered the three-dimensional waveequation. The Euler–Lagrange equation was developed in...
associated wave phenomena. These waves are also applied to model the motion of highway traffic flows. In these flows, mass and momentum equations can be combined...
Saint-Venant equations (aka Dynamic waveequation), we get the also classical Diffusive waveequation and Kinematic waveequation. For the diffusive wave it is...
This article summarizes equations in the theory of waves. A wave can be longitudinal where the oscillations are parallel (or antiparallel) to the propagation...
component wave function, and hence the wave packet, are solutions of a waveequation. Depending on the waveequation, the wave packet's profile may remain constant...
light was thought to consist of waves of electromagnetic fields which propagated according to Maxwell's equations, while matter was thought to consist...
to model the wave propagation in marine sediments using fractional derivatives. The fractional Schrödinger equation, a fundamental equation of fractional...
Waveequation analysis is a numerical method of analysis for the behavior of driven foundation piles. It predicts the pile capacity versus blow count...
alternatives. Significantly, the combined wave function of the system and environment continue to obey the Schrödinger equation throughout this apparent collapse...
quantum mechanics, where the waveequation arises from the physics involved. In these cases, solutions to the waveequation resulting in imaginary propagation...
are called the "momentum equations" instead. Equations of wave motion are called waveequations. The solutions to a waveequation give the time-evolution...
have constant amplitude. Equation (1) still describes the standing wave pattern that can form on this string, but now Equation (1) is subject to boundary...
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