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The group velocity is positive (i.e., the envelope of the wave moves rightward), while the phase velocity is negative (i.e., the peaks and troughs move leftward). The group velocity of a wave is the velocity with which the overall envelope shape of the wave's amplitudes—known as the modulation or envelope of the wave—propagates through space.
The group delay and phase delay properties of a linear time-invariant (LTI) system are functions of frequency, giving the time from when a frequency component of a time varying physical quantity—for example a voltage signal—appears at the LTI system input, to the time when a copy of that same frequency component—perhaps of a different physical phenomenon—appears at the LTI system output.
Phase and group velocity divided by 4 √ gσ / ρ as a function of inverse relative wavelength 1 / λ √ σ / ρg. Blue lines (A): phase velocity c p, Red lines (B): group velocity c g. Drawn lines: gravity–capillary waves. Dashed lines: gravity waves. Dash-dot lines: pure capillary waves. Note: σ is surface tension in this graph.
Propagation of a wave packet demonstrating a phase velocity greater than the group velocity. This shows a wave with the group velocity and phase velocity going in different directions. The group velocity is positive, while the phase velocity is negative. [1] The phase velocity of a wave is the rate at which the wave propagates in any medium.
Behavioral momentum is a theory in quantitative analysis of behavior and is a behavioral metaphor based on physical momentum.It describes the general relation between resistance to change (persistence of behavior) and the rate of reinforcement obtained in a given situation.
The overall group velocity is positive, and the wave packet moves as it disperses. The inverse Fourier transform is still a Gaussian, but now the parameter a has become complex, and there is an overall normalization factor.
In optics, group-velocity dispersion (GVD) is a characteristic of a dispersive medium, used most often to determine how the medium affects the duration of an optical pulse traveling through it. Formally, GVD is defined as the derivative of the inverse of group velocity of light in a material with respect to angular frequency , [ 1 ] [ 2 ]
Slow light refers to a very low group velocity of light. If the dispersion relation of the refractive index is such that the index changes rapidly over a small range of frequencies, then the group velocity might be very low, thousands or millions of times less than c, even though the index of refraction is still a typical value (between 1.5 and ...