Table of Contents
- 1 What is the difference between group and phase velocity?
- 2 How do you determine phase velocity?
- 3 What do you mean by phase velocity?
- 4 What do you understand by phase velocity?
- 5 Which of the following is correct relation between the group velocity and phase velocity?
- 6 How is group velocity different from the velocity of an individual wave within the group?
- 7 What is group velocity?
What is the difference between group and phase velocity?
Phase velocity is defined for both, the single waves and superimposed waves. The group velocity is defined only to the superimposed waves. The group velocity is the velocity of the wave with lower frequency, but the phase velocity is the velocity of the wave with higher frequency.
How do you find phase velocity and group velocity?
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. A wave of any shape will travel undistorted at this velocity.
How do you determine phase velocity?
For this reason, phase velocity is defined as v p = ω / k . This relation is generalized to three dimensions in Eq. (59). Given the phase velocity, the phase refractive index np is the factor describing how much slower the phase is propagating than the speed of light c0.
What is the difference between phase velocity and velocity?
The phase velocity (wave velocity) of a wave is the velocity with which any given phase of the wave travels. So, the phase velocity equals to the group velocity. For example, the phase velocity is equal to the group velocity when sound waves travel through the air as air is a non- dispersive medium for sound waves.
What do you mean by phase velocity?
Definition of phase velocity : the velocity of a wave motion as determined by the product of the wavelength and frequency. — called also wave velocity.
How do you calculate group velocity dispersion?
The group velocity dispersion is the group delay dispersion per unit length. The basic units are s2/m. For example, the group velocity dispersion of fused silica is +35 fs2/mm at 800 nm and −26 fs2/mm at 1500 nm. Somewhere between these wavelengths (at about 1.3 μm), there is the zero-dispersion wavelength.
What do you understand by phase velocity?
The phase velocity of a wave is the rate at which the wave propagates in any medium. This is the velocity at which the phase of any one frequency component of the wave travels. For such a component, any given phase of the wave (for example, the crest) will appear to travel at the phase velocity.
What is group velocity expression?
The group velocity is velocity of the envelope. For two waves group velocity is defined by vgroup = Δω / Δk where Δω = ω1 – ω2 and Δk = k1 – k2. This expression for group velocity is the slope of a frequency versus wavenumber graph.
Which of the following is correct relation between the group velocity and phase velocity?
Which of the following is the correct relation between the group velocity and the phase velocity? Explanation: The relation between the phase velocity and the group velocity is given by: vg = vp – λdvp/dλ. Thus, when dvp/dλ = 0, vg = vp.
How are phase and group velocity related for a monochromatic wave?
As this formula predicts, if the phase velocity does not depend on the wavelength of the propogating wave, then vg = vp. For example, a monochromatic wave with angular frequency ω = 2πν (ν is the frequency) travelling in +ve x-direction is given by, y = Asin(ωt – kx).
How is group velocity different from the velocity of an individual wave within the group?
Briefly, phase velocity refers to the velocity of a monochromatic wave, let’s say, the velocity of one of the peaks of the wave. On the other hand, group velocity refers to a group composed of waves within a frequency band ∆ω. Group velocity is the velocity with which the entire group of waves would travel.
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 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.
What is phase speed?
phase speed. phase velocity. noun. physics the speed at which the phase of a wave is propagated, the product of the frequency times the wavelength. This is the quantity that is determined by methods using interference.