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2
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1answer
29 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 ...
1
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3answers
70 views

Derivation of the group velocity

I know that the group velocity of a light pulse is defined as $$\begin{split}v_g&=v_p\left(1+\frac{\lambda}{n}\frac{dn}{d\lambda}\right)\\ ...
4
votes
1answer
47 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 ...
3
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5answers
1k 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 ...
0
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0answers
42 views

What happens to the group and phase velocity of light as it travels through a medium?

We have all been told that when light travels from, say, a vacuum through water it slows down. What I want to know is what happens to its phase velocity and group velocity. Refractive index is $n = ...
0
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1answer
72 views

What is meant by 'Phase velocity is $c^2/v$' [closed]

Is phase velocity $c^2/v$ or $v/2$? Is there only one phase velocity as indicated by the above formula? If yes then why is wavepacket said to be superposition of 'waves' whose velocity is termed as ...
1
vote
1answer
29 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 ...
1
vote
1answer
77 views

Why phase velocity of light is slower in a dielectric than vacuum?

Why does light speed suffer a reduction when it passes through a homogeneous dielectric medium? I know my math says so, i.e.- a highly polarizable ($\chi$) medium is associated with high $\epsilon$ ...
2
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1answer
64 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 ...
0
votes
0answers
123 views

Is velocity of de broglie wave faster than light? [duplicate]

In one of the properties of matter waves is that it can travel faster than light. In my test I was asked to prove this. There are derivations of both can travel faster then $c$ cannot faster than ...
0
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0answers
47 views

phase velocity in dielectric lined waveguide

I want to simply calculate the phase velocity of a mode in a dielectric loaded waveguide but am having difficulty arriving at a sensible answer. Here I consider only a TM mode. The problem is ...
1
vote
1answer
170 views

Klein-Gordon equation and wave velocity

It looks like solutions of the KG eqn travel faster than light, because if $$\omega^2 - k^2 = m^2$$ then $$\mid\ \omega\mid \ > \ \mid k\ \mid$$ and I thought the wave velocity was $\omega / k$. ...
7
votes
4answers
547 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 ...
0
votes
0answers
2k views

Relationship between phase velocity and group velocity with 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 ...
1
vote
0answers
92 views

How to find the speed of sound in a monoatomic crystal

My question is about phase and group velocities in a monoatomic crystal. I want to find the speed of sound, so I am using the equation for vibrational modes: ...
1
vote
1answer
1k 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 ...
1
vote
0answers
110 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?
1
vote
3answers
141 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 ...
0
votes
0answers
282 views

Wave Packets, Group velocity, and Phase velocity [duplicate]

Mathematically, you find that the wave function of a particle $\Psi (x,t)$ moves with the same velocity as the velocity of the particle ($v_{particle} = v_{group}$). Is there a reason why the ...
3
votes
3answers
609 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?
0
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0answers
31 views

Learning about group velocity, phase velocity and particle velocity [duplicate]

I am studying quantum physics and I would like to know a bit more in detail about group velocity, particle velocity and phase velocity. Can you guys suggest some books/online resources where I can ...
0
votes
1answer
209 views

How can we calculate (relativisticly correct) ratio $\lambda_e/\lambda_p$ if proton and electron have same speeds

This question is about group/phase velocities and also De Brogilie wavelength. What I would like to know is how to derive ratio $\lambda_e/\lambda_p$ ($\lambda_e$ and $\lambda_p$ are De Broglie ...
2
votes
3answers
1k views

Two different mediums can have equal index of refraction?

In other words: given a certain medium, is light's phase velocity unique?
2
votes
1answer
5k 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 ...
7
votes
1answer
7k 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 ...
1
vote
2answers
4k 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 ...
0
votes
1answer
288 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 ...
4
votes
2answers
5k 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?
5
votes
7answers
566 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 ...
2
votes
2answers
1k 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 ...
4
votes
1answer
395 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 ...
1
vote
1answer
419 views

Why doesn't anomalous dispersion allow faster-than-light propagation?

It seems that the phase velocity of light could be greater than $c$, if $\sqrt{\epsilon \mu} < 1/c$, i.e. for anomalous dispersion. Are there examples of such media? For diamagnetics it seems ...
19
votes
3answers
3k views

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 ...
1
vote
3answers
9k 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.
6
votes
3answers
384 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 ...