What is the difference between phase velocity and group velocity?
What is the difference between phase velocity and group velocity?
The phase velocity is the velocity of the wave with higher frequency. The group velocity is the velocity of the wave with lower frequency.
Which is greater group velocity or phase velocity?
For most substances, therefore, the group velocity is smaller than the phase velocity. In such cases, it is mathematically possible that the group velocity may be larger than the phase velocity.
What is the relation between group and phase velocity?
Group Velocity And Phase Velocity Relation The group velocity is directly proportional to phase velocity.
In which medium phase velocity and group velocity are equal?
Dispersion. When these two monochrome waves are propagating in vacuum, they have the same phase velocity c (the speed of light in vacuum), and the superposed wave’s phase velocity equals its group velocity(both are c).
Why are phase and group velocity not the same in waveguide?
First, because fmn takes on different values for different modes, group velocity is different for different modes. Specifically, higher-order modes propagate more slowly than lower-order modes having the same frequency.
Is phase velocity half of group velocity?
What is the phase and group velocity for a sinusoidally-varying wave in this material? Thus, we see that in this case the group velocity is always half the phase velocity. Another commonly-encountered example for which vg is not necessarily equal to vp is the propagation of guided waves; e.g., waves within a waveguide.
Which of the following is the correct relation between the group velocity and the phase velocity in a dispersive medium?
In a dispersive medium, the group velocity is less than the phase velocity only. Group velocity is defined as: V g r o u p = ω 2 − ω 1 k 2 − k 1 = d ω d k . Dispersion is when the distinct phase velocities of the components of the envelope cause the wave packet to “Spread out” over time.
Can group velocity and phase velocity be the same?
The phase velocity is: vp = ω/k. The function ω(k), which gives ω as a function of k, is known as the dispersion relation. If ω is directly proportional to k, then the group velocity is exactly equal to the phase velocity.
Why phase velocity is faster than speed of light?
So if you interfere two plane waves propagating in opposite directions, but off by a fraction of a degree from being exactly opposite, the interference pattern will produce humps that propagate faster than the speed of light.
Can phase velocity be faster than light speed?
The phase velocity vp can be less than the speed of light. It can also be greater than the speed of light, but this does not violate special relativity because the single monochromatic wave or constant oscillation does not carry energy or information.
Is phase velocity and wave velocity same?
Wave velocity, when not otherwise specified, usually means the phase velocity: the rate at which the phase travels in space. This site animates the differences between phase and group velocities. The group velocity is the speed at which energy is transported.
Why group velocity is less than phase velocity in dispersive medium?
Hence, the group velocity is less than the phase velocity Dispersion is when the distinct phase velocities of the components of the envelope cause the wave packet to “Spread out” over time.
