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Wave speed is a wave property, which may refer to absolute value of: . phase velocity, the velocity at which a wave phase propagates at a certain frequency; group velocity, the propagation velocity for the envelope of wave groups and often of wave energy, different from the phase velocity for dispersive waves
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.
In the context of electromagnetics and optics, the frequency is some function ω(k) of the wave number, so in general, the phase velocity and the group velocity depend on specific medium and frequency. The ratio between the speed of light c and the phase velocity v p is known as the refractive index, n = c / v p = ck / ω.
Dispersion occurs when sinusoidal waves of different wavelengths have different propagation velocities, so that a wave packet of mixed wavelengths tends to spread out in space. The speed of a plane wave, , is a function of the wave's wavelength : = ().
is the speed of light (i.e. phase velocity) in a medium with permeability μ, and permittivity ε, and ∇ 2 is the Laplace operator. In a vacuum, v ph = c 0 = 299 792 458 m/s, a fundamental physical constant. [1] The electromagnetic wave equation derives from Maxwell's equations.
A sinusoidal wave, of small surface-elevation amplitude and with a constant wavelength, propagates with the phase velocity, also called celerity or 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.
Consider a 2.5 kilometer homogeneous arterial segment that follows a triangular fundamental diagram as shown in figure 2. Figure 2. Fundamental diagram for the example This corridor is divided into 30 cells and is simulated for 480 seconds with a time step of 6 seconds.
For an incident wave traveling from one medium (where the wave speed is c 1) to another medium (where the wave speed is c 2), one part of the wave will transmit into the second medium, while another part reflects back into the other direction and stays in the first medium. The amplitude of the transmitted wave and the reflected wave can be ...