Questions tagged [phase-velocity]
The phase-velocity tag has no usage guidance.
55
questions
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Is the phase velocity of plane wave solutions of the Klein-Gordon equation larger than $c$?
The phase velocity is given by
$$ v= \frac{\omega}{k} \, .$$
Using the usual dispersion relation
$$ E^2 = p^2c^2+ m^2c^4 \leftrightarrow \omega^2 \hbar^2= k^2\hbar^2 c^2 + m^2c^4$$
yields
$$ v= \frac{\...
2
votes
2answers
39 views
Is the group velocity times the phase velocity always the velocity of light squared?
Can there be cases where it is different from $c$ squared? If so in what situations would it differ?
7
votes
1answer
301 views
Seeming violation-wave travelling faster than speed of light
Consider the basic relation $$E=\sqrt{(pc)^2+(mc^2)^2}.$$
Every particle possesses a wave nature and it depends on the situation in which one among the two is perceptible...
Consider a particle with ...
1
vote
0answers
40 views
Wave packet - phase vs group velocity
So, I've been revising QM recently and the concept of group vs phase velocity has me confused.
Let's say we have a wave packet. As quoted in Griffiths, "...A wave packet is a superposition of ...
3
votes
2answers
96 views
What does phase velocity physically represent, and why can it be superluminal? [duplicate]
Phase velocity is defined as $v_p=\frac{\omega}{k}$ and is described in various textbooks as being the speed at which the phase of a wave propagates. If you have a wave train that is modulated by an ...
0
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0answers
21 views
Waves velocity for a standing wave of a string
I have done a laboratory experience to determine the speed of propagation of a wave in a vibrating magnetic string. To calculate the frequency (f) of oscillation I used an oscilloscope that calculated ...
-1
votes
1answer
52 views
Wave packet in dispersive medium, how will the group velocity be affected? [closed]
A wave packet with center frequency ω is propagating in dispersive medium with phase velocity of 1.5 x 10^3 m/s. When the frequency ω is increased by 2%, the phase velocity is found to decrease by 3%. ...
0
votes
0answers
38 views
Group and phase velocity for a superposition of 2 monochromatic waves
A wave packet in one dimension with a dispersion relation $\omega$ is a function of the form:
$$f(x,t):=\sum_{i=1}^n\lambda_i\exp[i(k_i x+\omega[k_i] t)]\hspace{1cm}\forall i\leq n\colon\lambda_i,k_i\...
4
votes
2answers
152 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 ...
0
votes
2answers
656 views
Phase Velocity Derivation
I spend few hours trying to derive phase velocity of sinusoidal wave $$\cos(kx - \omega t).$$ I know that it must be equal to $\omega \over k$ but after banging my head for few hours and trying to ...
3
votes
2answers
126 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. ...
1
vote
2answers
522 views
Wave group and phase velocities
When talking about phase velocity and group velocity they tend to be both expressed in terms of another $v$. From my understanding this $v$ comes from the wave equation, but what does it represent? ...
3
votes
1answer
71 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.
0
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0answers
34 views
How is the phase velocity for a wave in a stringed instrument derived?
I was searching on the internet for a formula relating velocity of wave and force of tension of a string (eg how the tension in a string instrument effects the velocity) and this formula keeps ...
2
votes
1answer
864 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?
2
votes
1answer
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:
$$
\begin{align}
v & = \frac{\omega}{k} \tag{1} \\[10px]
v & = \sqrt{\frac{T}{u}} \tag{2}
\end{align}
$$
...
1
vote
1answer
217 views
Is quantum velocity generally equal to group velocity?
It is often said that the velocity operator in quantum mechanics identifies the group velocity. Here's the argument: for the free particle, we have $\omega = \hbar k^2/2m$ and the (quantum) velocity ...
2
votes
1answer
197 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, ...
1
vote
2answers
85 views
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 ...
1
vote
1answer
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 ...
4
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0answers
92 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-...
0
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0answers
123 views
Calculation of Phase Delay of a Curved Planar Dielectric Waveguide (i.e., bend)
I am working on a very phase sensitive planar dielectric waveguide device and I need to calculate the phase delay induced by a bend of some radius, $r$ and of $\phi$ radians for a give planar ...
1
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0answers
125 views
Is disturbance propagation velocity equal to wave velocity in a solid body?
How do the disturbance propagation velocity and wave propagation velocity relate to each other?
To explain my question in details I will describe the following situation from the theory of acoustic ...
-1
votes
1answer
443 views
Interpreting group velocity of free particle wave packet
I am trying to understand the concept of group velocity of a free particle wave packet: $$\Psi(x,t) = \frac{1}{\sqrt{2 \pi}}\int_{-\infty}^{\infty} \phi(k)e^{ikx}e^{-\frac{i \hbar k^2 t}{2m}}dk.$$
...
3
votes
1answer
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'...
0
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3answers
2k 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)\\
&=\frac{c}{n}\left(1+\frac{\lambda}{n}\frac{dn}{d\...
4
votes
1answer
100 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
...
4
votes
5answers
4k 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 ...
-1
votes
1answer
735 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 ...
2
votes
3answers
746 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
351 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
498 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 ...
1
vote
2answers
754 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$$
and I thought the wave velocity was $\omega / k$.
...
8
votes
4answers
744 views
Does radiation force depend on group velocity or on phase velocity?
What is the radiation force $F$ due to a beam of photons of power $P$ undergoing perfect reflection? Is it
$$a) F = 2 P / c$$
or
$$b) F = 2 P / v_g$$
where $v_g$ is the group velocity
?
Note that ...
2
votes
1answer
11k views
Relationship between phase velocity and group velocity using the de Broglie postulates
If I have to show that the group velocity of a free particle is twice the phase velocity, is the following argument correct (avoiding to use the wave function and the momentum operator):
For a ...
2
votes
2answers
6k views
Phase velocity greater then the speed of light?
It is my understanding the the phase velocity of a wave can be greater then the speed of light. So imagine we had a wave packet consisting of a single sinusoidal wave;
$$y=\sin(\omega t-kx)$$
Then ...
asked Mar 7 '15 at 8:16
Quantum spaghettification
1,3267 gold badges31 silver badges96 bronze badges
2
votes
0answers
221 views
Phase and group velocity of a soliton? [closed]
How do I find the phase velocity and group velocity of a soliton with a $\operatorname{sech}$ (hyperbolic secant) envelope?
2
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3answers
823 views
Derviation of group velocity
I am working thru a derivation of the group velocity formula and I get to this stage:
$$y=2A\cos(x\frac{\Delta K}{2} -t\frac{\Delta \omega}{2})\sin( \bar k x-\bar \omega t)$$
Then all the derivations ...
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0answers
831 views
Wave Packets, Group velocity, and Phase velocity [duplicate]
Mathematically, you find that the wave function of a particle $\Psi (x,t)$ moves with the same velocity as the velocity of the particle ($v_{particle} = v_{group}$).
Is there a reason why the ...
3
votes
3answers
2k views
Why is the phase velocity used in the definition of the refractive index?
I'm aware of the so-called group index but why is the phase velocity used in the standard definition of the index of refraction? What advantage does this offer?
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0answers
41 views
Learning about group velocity, phase velocity and particle velocity [duplicate]
I am studying quantum physics and I would like to know a bit more in detail about group velocity, particle velocity and phase velocity.
Can you suggest some books/online resources where I can learn ...
0
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1answer
515 views
How can we calculate (relativisticly correct) ratio $\lambda_e/\lambda_p$ if proton and electron have same speeds
This question is about group/phase velocities and also De Brogilie wavelength.
What I would like to know is how to derive ratio $\lambda_e/\lambda_p$ ($\lambda_e$ and $\lambda_p$ are De Broglie ...
2
votes
3answers
3k views
Two different mediums can have equal index of refraction?
In other words: given a certain medium, is light's phase velocity unique?
5
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2answers
12k views
Deriving group velocity
At the introduction to quantum mechanic phase $v_p$ and group $v_g$ velocities are often presented. I know how to derive $v_p$ and get equation:
$$
\scriptsize
v_p=\frac{\omega}{k}.
$$
What i dont ...
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votes
1answer
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 ...
2
votes
2answers
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 ...
1
vote
1answer
414 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 ...
4
votes
2answers
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?
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7answers
893 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 ...
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2answers
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 ...
