The phase velocity of a wave is the rate at which the wave propagates in any medium. This is the velocity at which the phase of any one frequency component...

the leading edge of the group. The idea of a group velocity distinct from a wave's phase velocity was first proposed by W.R. Hamilton in 1839, and the...

dispersion relation, one can calculate the frequency-dependent phase velocity and group velocity of each sinusoidal component of a wave in the medium, as a...

are two velocities that are associated with waves, the phase velocity and the group velocity. Phase velocity is the rate at which the phase of the wave...

phase speed. While the phase velocity is a vector and has an associated direction, celerity or phase speed refer only to the magnitude of the phase velocity...

classical velocity of the particle. The group velocity is the (approximate) speed at which the whole wave packet propagates, while the phase velocity is the...

reverse of the electromagnetic wave, characterized by an antiparallel phase velocity is also an indicator of negative index of refraction. Furthermore, negative-index...

{\displaystyle \mathbf {v} } is the velocity of the center of mass of the particle, identical to the group velocity. The phase velocity in isotropic media is defined...

{1}{v}}.} The phase velocity is the speed at which the crests or the phase of the wave moves, which may be different from the group velocity, the speed at...

dielectric medium (such as distilled water) at a speed greater than the phase velocity (speed of propagation of a wavefront in a medium) of light in that medium...

capillary wave is a wave traveling along the phase boundary of a fluid, whose dynamics and phase velocity are dominated by the effects of surface tension...

motion. Four-velocity (relativistic version of velocity for Minkowski spacetime) Group velocity Hypervelocity Phase velocity Proper velocity (in relativity...

the distance Δx is related to the time interval Δt by the so-called phase velocity vp v p = Δ x Δ t = λ f   . {\displaystyle v_{\rm {p}}={\frac {\Delta...

opposition of wave vector to group velocity, and energy to velocity. "Phase velocity" is used conventionally, as phase velocity has the same sign as the wave...

flows through a given conductor such as a wire or cable at a particular phase velocity v p {\displaystyle v_{p}} . It takes time for later portions of the...

number k. Numerical methods are used to find the phase velocity cp = fλ = ω/k, and the group velocity cg = dω/dk, as functions of d/λ or fd. cl and ct...

fluid velocity (excluding the other phase, solids, etc.), m/s. The local physical velocity can still be different than the average fluid velocity because...

pressure oscillations that are either in-phase or anti-phase, respectively. This results in the phase velocity of any given fast mode always being greater...

the group velocity of a deep water wave is half of its phase velocity, which, in turn, goes as the square root of the wavelength. Two velocity parameters...

deal with a phase velocity or group velocity faster than the vacuum velocity of light. However, as stated above, a superluminal phase velocity cannot be...

wave propagation in general, dispersion is the phenomenon in which the phase velocity of a wave depends on its frequency; sometimes the term chromatic dispersion...

Gouy phase at z, an extra phase term beyond that attributable to the phase velocity of light. The physical electric field is obtained from the phasor field...

amplitude decreases as the wave propagates in the x direction. Wavelength, phase velocity, and skin depth have simple relationships to the components of the propagation...

cancellation Phase problem Phase spectrum Phase velocity Phasor Polarization (waves) Coherence (physics), the quality of a wave to display a well defined phase relationship...

refraction θ 2 {\displaystyle {\theta _{2}}} is equal to the ratio of phase velocities v 1 v 2 {\textstyle {\frac {v_{1}}{v_{2}}}} in the two media, or equivalently...

traveling ionospheric disturbances and could be observed by radars. The phase velocity c {\displaystyle c} of a linear gravity wave with wavenumber k {\displaystyle...

velocities can exceed c. The phase velocity of X-rays through most glasses can routinely exceed c, but phase velocity does not determine the velocity...

were two velocities of light, the phase velocity and the group velocity. The phase velocity can in fact be greater than c, but the group velocity, being...

time-varying amplitude does not propagate at the phase velocity but rather at the group velocity. The group velocity depends not only on the refractive index...

carrier waves, phase velocity, and group velocity – date from the mid-1800s. The idea of a group velocity distinct from a wave's phase velocity was first proposed...