# Questions tagged [phase-velocity]

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### In superluminal phase velocities, what is it that is traveling faster than light?

I understand that information cannot be transmitted at a velocity greater than speed of light. I think of this in terms of the radio broadcast: the station sends out carrier frequencies $\omega_c$ but ...
15k views

### Phase and Group Velocity of Electromagnetic Waves

Moving charges produce oscillating electric and magnetic fields -we have an electromagnetic wave. In terms of moving charges or at the level of charges, what is phase velocity and group velocity of ...
740 views

### Does radiation force depend on group velocity or on phase velocity?

What is the radiation force $F$ due to a beam of photons of power $P$ undergoing perfect reflection? Is it $$a) F = 2 P / c$$ or $$b) F = 2 P / v_g$$ where $v_g$ is the group velocity ? Note that ...
492 views

### Controllable faster-than-light phase velocity

This is not another question about faster-than-light travel or superluminal communication. I totally appreciate the speed limit capped by physical laws (or theories.) Just curious, since there is no ...
12k views

### Deriving group velocity

At the introduction to quantum mechanic phase $v_p$ and group $v_g$ velocities are often presented. I know how to derive $v_p$ and get equation: $$\scriptsize v_p=\frac{\omega}{k}.$$ What i dont ...
881 views

### Information relationship to Special Relativity

How do we write mathematically that "information" cannot go faster than light? And along a similar line of thought, how do we relate "information" with special relativity. Lastly, what is the ...
523 views

### Fermat principle: which index of refraction?

I am somewhat puzzled by a common formulation of the Fermat principle (light travel time), because it contains index of refraction related to phase velocity while light travel time through a slab of ...
3k views

### Group and phase velocity - why can the latter be faster than light? [duplicate]

The phase velocity can be faster than light. Some argue that the phase velocity doesn't convey information, but this doesn't convince me. We can emit a wave of a single one frequency. Then it will ...
140 views

### What really is the speed of light in a medium/vacuum, group or phase velocity?

While reading about refractive index 2 terms popped up, group velocity which alway slows down in a medium and phase velocity which may exceed speed of light. Say in a complete vacuum and using laser ...
99 views

### anticausal group velocity?

https://en.wikipedia.org/wiki/Anomalous_dispersion claims: Recently, it has become possible to create gases in which the group velocity is not only larger than the speed of light, but even ...
9k views

### Group Velocity and Phase Velocity of Matter Wave?

In quantum mechanics, what is the difference between group velocity and phase velocity of matter wave? How can it also be that phase velocity of matter wave always exceeds the speed of light?
2k views

### Why is the phase velocity used in the definition of the refractive index?

I'm aware of the so-called group index but why is the phase velocity used in the standard definition of the index of refraction? What advantage does this offer?
111 views

### Why we do not use $v=f \lambda$ for the waves associated with particles?

As the waves travel with velocity $$v= f \lambda,$$ where $v$ is velocity, $f$ is frequency and $\lambda$ is wavelength. Here we can see that velocity of wave is directly proportional to wavelength. ...
2k views

### Wave Velocity vs. Phase Velocity

I am trying to understand the difference between 'wave velocity' and 'phase velocity'. I know that generally they are equal, but when is that not the case? I, of course, tried to google it, and didn'...
66 views

### Why is refractive index equals to speed of light upon phase velocity and not group velocity?

We have been using group velocity for most purposes as its the velocity with which the wave packet travels, they why do we use phase velocity for calculating refractive index.
87 views

### Characteristics of wavepackets

I've been learning about wave packets and group velocities recently and had a question. Using simple trigonometric identies, we can show that the super position of two traveling waves with frequency-...
3k views

### Two different mediums can have equal index of refraction?

In other words: given a certain medium, is light's phase velocity unique?
17k views

### How do you find the velocity function of a mechanical wave?

With the form $y(x,t)=A\sin(kx-\omega t+\phi_0)$, there are two variables, How do I find the velocity? I don't know I can apply derivative with two variables.
783 views

### Derviation of group velocity

I am working thru a derivation of the group velocity formula and I get to this stage: $$y=2A\cos(x\frac{\Delta K}{2} -t\frac{\Delta \omega}{2})\sin( \bar k x-\bar \omega t)$$ Then all the derivations ...
467 views

### Confusion in phase and group velocity

This question is based on this question asked in physics SE. In this question, they say that phase velocity greater than velocity of light. Ok, greater than velocity of light for phase velocity is ...
6k views

### What does the velocity of a wave mean?

I know that the velocity of a wave is given by $v=\lambda f$ but what does this velocity represent in the physical sense. For instance, if I am told a car moves at a velocity of 5 $m/s$ I know that ...
2k views

### Rotating mirror - Foucault's measurement of light speed

Some time ago I came across a secondary web source on measurement of light speed in water made by Foucault around 1850. I append its redrawn scheme below (light is reflected from the rotating mirror ...
79 views

### What does phase velocity physically represent, and why can it be superluminal? [duplicate]

Phase velocity is defined as $v_p=\frac{\omega}{k}$ and is described in various textbooks as being the speed at which the phase of a wave propagates. If you have a wave train that is modulated by an ...
7k views

### Are these definitions for transverse wave velocity on a string consistent?

I've found two definitions for the velocity of a transverse wave on a stretched string: \begin{align} v & = \frac{\omega}{k} \tag{1} \\[10px] v & = \sqrt{\frac{T}{u}} \tag{2} \end{align} ...
190 views

### Linear polarization and phase

In this discussion of polarization, it says For linearly polarized light, the $x$- and $y$-components are exactly in phase and therefore rise and fall together Can it therefore be assumed, then, ...
11k views

### Relationship between phase velocity and group velocity using the de Broglie postulates

If I have to show that the group velocity of a free particle is twice the phase velocity, is the following argument correct (avoiding to use the wave function and the momentum operator): For a ...
715 views

### Why the relationship $v_p v_g = c^2$ (phase velocity multiply group velocity equals lightspeed squared) exists in waveguide structures?

What’s the reason that the relationship of de Broglie hypothesis(hypothesis-->relations) will hold in Waveguide structures?
724 views

### How can pressure and velocity fluctuations in acoustic plane waves be in phase and still hold to the B.C. that velocity must be zero at a solid wall?

In linear plane-wave acoustics (no mean flow, small perturbations, etc.), it is often derived that the phase of a traveling pressure fluctuation wave and a fluctuation velocity wave are the same. For ...
221 views

### Phase and group velocity of a soliton? [closed]

How do I find the phase velocity and group velocity of a soliton with a $\operatorname{sech}$ (hyperbolic secant) envelope?
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### Meanings of the word “phase”

I have been confused at points due to multiple uses of the word "phase". Mainly, when I think of a phase diagram, I think of a graph relating temperature to pressure, and segments the possible ...
5k views

### Phase velocity greater then the speed of light?

It is my understanding the the phase velocity of a wave can be greater then the speed of light. So imagine we had a wave packet consisting of a single sinusoidal wave; $$y=\sin(\omega t-kx)$$ Then ...
65 views

### For light in a medium, can phase information be extracted from envelope slowdown?

Can phase information be extracted from envelope slowdown? That is, if I can track the envelope of a pulse of light as it travels through a medium, but I can't see the phase of that pulse (maybe the ...
413 views

### Wavefronts and phase velocity faster than $c$

Lets assume we have parallel wavefronts in a glass of water: and we put an inclined rod on the water surface: related to a very small inclining, Vy velocity is greater or much greater then Vx (Vy ...
337 views