Phase, Group, and Signal Velocity. The velocity of a wave can be defined in many different ways, partly because there many different kinds of waves, and partly. Phase and Group Velocity. Phase Velocity. The phase velocity of a wave is the rate at which the phase of the wave propagates in space. This is the velocity at. more information on The distinction between the phase velocity and the group velocity of a wave is a concept of general significance for.
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Phase and Group Velocity
The group velocity is positive, while the phase velocity is negative. This is the velocity at which the phase of any one frequency component of the wave travels.
Any modulation will propagate at the group velocity, which, in dispersive media, is always less than c. An example of an actual physical application in which we must be careful to distinguish between the phase and the group velocity is the case of electromagnetic waves propagating through a hollow magnetic conductor, often called a phase group velocity.
This is roughly analogous to how the pipes in a Church organ will sustain only certain resonant patterns. Unfortunately we frequently read in the newspapers about how someone has succeeded in transmitting a wave with a group velocity exceeding c, and we are asked to regard this as an astounding discovery, overturning the phase group velocity of relativity, etc.
The problem with these stories is that the group velocity corresponds to the actual signal velocity only under conditions of normal dispersion, or, more generally, under conditions when the group velocity is less than the phase velocity. In other circumstances, the group velocity does not necessarily represent the actual propagation speed of any information or energy.
What is the difference between phase velocity and group velocity? - Quora
phase group velocity For example, in a regime of anomalous dispersion, which means the refractive index decreases with increasing wave number, the preceding formula shows that what we called the group velocity exceeds what we called the phase velocity.
In such circumstances the group velocity no longer represents the speed at which information or energy propagates.
To see why the group velocity need not correspond to the speed of information in a wave, notice that in general, by superimposing simple phase group velocity with different frequencies and wavelengths, we can easily produce a waveform with a group velocity that is arbitrarily great, even though the propagation speeds of the constituent waves are all low.
A phase group velocity of such a case is shown below.
Nevertheless, phase group velocity clear that no information can be phase group velocity faster than the phase speeds of the constituent waves A and B. This is just one illustration of how simple interfering phase effects can be mis-construed as ultra-high-speed signals.
In fact, by simply setting kA to 2. The phase velocity is the the wave speed of the wave.
For physically unrealisable solutions this might be great than speed of light as well which violates relativity. But as the function isn't physically phase group velocity it's fine. The carrier wave the blue line travels at the phase velocity and is given by u2. The wave packet moves at the group velocity.
It is the envelope which carries information. Group velocity and phase velocity are not necessarily the same.
Group velocity - Wikipedia
Group velocity is given by, Phase and group velocity are related through Rayleigh's formula, If the derivative term is zero, group velocity equals phase velocity.
In this case, there is no phase group velocity. Dispersion is when the distinct phase velocities of the components of the envelope cause the wave packet to "spread out" over time.