Table of Contents
Is phase velocity greater than group 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.
Can phase velocity be less than C?
yes it can and in waveguides with air or vacuum the electromagnetic waves always have a phase velocity faster than c. There is no violation of any physics law as this velocity does not represent information or energy. Yes.
How do you find group velocity from phase velocity?
Since each amplitude envelope contains a group of internal waves, this speed is usually called the group velocity, vg. In a given medium, the frequency is some function ω(k) of the wave number, so in general, the phase velocity vp= ω/k and the group velocity vg = dω/dk depend on the frequency and on the medium.
What is VP and VG?
Generally, ω(k) is called the dispersion relation and indicates the dispersion properties of a medium. As this formula predicts, if the phase velocity does not depend on the wavelength of the propogating wave, then vg = vp. Phase velocity of sound waves is independent of the wavelength when it propogates in air.
Can phase velocity be infinite?
Energy transport is limited to the speed of light, according to Einstein’s laws, but there are no physical limitations on the phase velocity. When it reaches zero, meaning there is no movement of the peaks and valleys of the wave, the phase velocity becomes infinite, making the wavelength of light nearly infinite.
Is phase velocity speed of light?
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.
What do you mean by group velocity?
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.
What exactly is phase velocity?
The phase velocity is defined as the velocity for a single-wavelength wave, whereas the group velocity is defined as the velocity for a packet of waves in which the waves vary in wavelength.
What is the difference between phase and group velocity?
The group velocity is often equal to the information velocity, but that is not always true. Also, the group velocity is not always less than the phase velocity. The group velocity can be much, much less than c (~10 m/s), equal to c, greater than c, or even negative.
What does phase velocity mean?
Phase velocity. The phase velocity of a wave is the rate at which the phase of the wave propagates in space.
What is a velocity group?
Group velocity. The group velocity of a wave is the velocity with which the overall shape of the wave’s amplitudes—known as the modulation or envelope of the wave—propagates through space. For example, if a stone is thrown into the middle of a very still pond, a circular pattern of waves with a quiescent center appears in the water,…
What is group velocity?
The group velocity of a wave is the velocity with which the overall shape of the wave’s amplitudes—known as the modulation or envelope of the wave—propagates through space.