What is the formula for 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 K in phase velocity?

where ω is the wave’s angular frequency (usually expressed in radians per second), and k is the angular wavenumber (usually expressed in radians per meter). The phase velocity is: vp = ω/k.

What is the phase velocity of the particle?

The velocity v of the electron in the free electron gas model is the velocity with which the phase of the wave moves, it is called phase velocity vP. As long as a single plane wave symbolizes all that is to a particle, the phase velocity is automatically also the particle velocity v.

What is phase velocity group velocity?

Waves can be in the group and such groups are called wave packets, so the velocity with a wave packet travels is called group velocity. The velocity with which the phase of a wave travels is called phase velocity. The relation between group velocity and phase velocity are proportionate.

What is phase velocity in transmission lines?

Phase velocity is the propagation velocity of an equiphase wave surface of a single sinusoidal wave along a transmission line, and group velocity is the propagation velocity of the envelope of two sinusoidal waves with a slight difference in frequency superimposed.

What is difference between phase velocity and group velocity?

The Phase velocity refers to the velocity of a monochromatic wave. Group velocity is the velocity with which the entire group of waves would travel.

What is the difference between wave velocity and phase velocity?

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.

What is the speed of light underwater?

225,000 kilometers per second
Light travels at approximately 300,000 kilometers per second in a vacuum, which has a refractive index of 1.0, but it slows down to 225,000 kilometers per second in water (refractive index of 1.3; see Figure 2) and 200,000 kilometers per second in glass (refractive index of 1.5).

Is the phase velocity of a plasma wave equal to the speed of light?

The phase velocity of the plasma wave in the case of forward scattering is equal to the group velocity of the beat wave, which for low-density plasma is close to the speed of light, as can be seen from the relation: v ϕ = ω p / k p = Δω / Δk = v g = cη ∼ c where eqn and ω 2p ≪ ω 2 were used to show that η is close to unity.

Is the phase velocity twice the group velocity?

In this deep-water case, the phase velocity is twice the group velocity. The red square overtakes two green circles when moving from the left to the right of the figure. New waves seem to emerge at the back of a wave group, grow in amplitude until they are at the center of the group, and vanish at the wave group front.

Is the phase velocity of a wave positive or negative?

The group velocity is positive, while the phase velocity is negative. The phase velocity of a wave is the rate at which the phase of the wave propagates in space. This is the velocity at which the phase of any one frequency component of the wave travels.

Which is the associated wave number of a plasma?

According to the dispersion relation ( 1155 ), the associated wave-number is given by Indeed, it can be seen that for electromagnetic waves in a plasma take the form of decaying standing waves, rather than traveling waves.