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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 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.
Finally only in this case the superposition principle fully apply, i.e. the wave function in a point P can be expanded as a superposition of waves on a border surface enclosing P. Wave functions can be interpreted in the usual quantum mechanical sense as probability densities where the formalism of Green's functions and propagators apply. What ...
From the basic one-dimensional plane-wave solutions, a general form of a wave packet can be expressed as (,) = (()). where the amplitude A(k), containing the coefficients of the wave superposition, follows from taking the inverse Fourier transform of a "sufficiently nice" initial wave u(x, t) evaluated at t = 0: = (,) . and / comes from Fourier ...
Fermat's principle is most familiar, however, in the case of visible light: it is the link between geometrical optics, which describes certain optical phenomena in terms of rays, and the wave theory of light, which explains the same phenomena on the hypothesis that light consists of waves.
A shock wave is a type of propagating disturbance. When a wave moves faster than the local speed of sound in a fluid, it is a shock wave. Like an ordinary wave, a shock wave carries energy and can propagate through a medium; however, it is characterized by an abrupt, nearly discontinuous change in pressure, temperature and density of the medium ...
In fluid dynamics, Airy wave theory (often referred to as linear wave theory) gives a linearised description of the propagation of gravity waves on the surface of a homogeneous fluid layer. The theory assumes that the fluid layer has a uniform mean depth, and that the fluid flow is inviscid , incompressible and irrotational .
When I conceived the first basic ideas of wave mechanics in 1923–1924, I was guided by the aim to perform a real physical synthesis, valid for all particles, of the coexistence of the wave and of the corpuscular aspects that Einstein had introduced for photons in his theory of light quanta in 1905. —