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Group velocity, phase velocity and signal velocity for axion like particles

In dark matter models of axion-like particles (ALPs), sometimes we get the field $$\phi=2\phi_0\sin(m_\phi c^2 t/\hbar)\cos(k_\phi x)$$ This is like an stationary field with amplitude $\phi_0$ (in m/s ...
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The velocity of a quantum mechanical plane wave of a photon

There is a famous "derivation" or "demonstration" that is often presented in introductory classes in quantum mechanics. I find it deeply unsettling and I feel like key information ...
The Feadow's user avatar
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2 answers
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Phase difference in Michelson Interferometer

I'm currently taking a quantum mechanics course in university and our professor introduced us to the Michelson Interferometer (or at least what I believe is an apparatus based on it), where a light ...
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What does "non-dispersive" mean in terms of waves and group velocity?

I'm confused about the term wave group velocity: It is usually explained in terms of a superposition of harmonic waves with very closely spaced wave vectors and frequencies. It is then easily shown, ...
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Why the phase velocity of X-rays inside glass is faster than $c$?

For hard X-rays the refraction index of glass becomes slightly $n<1$ which means that the phase velocity (not group velocity) of X-rays inside glass is larger than $c$ the group velocity speed ...
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Can radiative transfer theory be used to calculate an effective index of refraction?

As I understand it, the (real) index of refraction is given by the ratio of speed of a monochromatic light wave in vacuo versus speed in medium. When it comes to the question of propagation of a light ...
roland's user avatar
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Coupled microstrip waveguide: Why do the even and odd modes have different wave velocities?

Why do the odd and even modes in a coupled microstrip waveguide have different phase velocities? Is this also the case for a coplanar strips waveguide?
janlite's user avatar
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How to calculate the phase velocity of a partial standing wave

Partial Standing Waves Partially Reflected Wave A traveling wave encountering an impedance change will be partially reflected and transmitted. It can be represented as the sum of the incident (...
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Why is the velocity of a wave given by $v=\lambda{}f$ different than differentiation?

As obvious from the nature of this question, I am a first-year physics student (with an absent lecturer), and I am having trouble grasping the concept of wave velocity. I've read these answers (1,2) ...
Jamie's user avatar
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3 votes
1 answer
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Confused about the Kelvin wake pattern

What are the $v_{\text{phase}}$ and the $v_{\text{group}}$ in Kelvin wakes? Additionally there are tons of water waves combined to form the kelvin wake. How is it possible for the $v_{\text{group}}$ ...
7Wdev's user avatar
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Is the observed speed of an infinite set of perfect ocean waves of constant amplitude and frequency independent of an observer's motion?

I am asking this question because it occurred to me that wave propagation has some generally under considered properties regardless and independent of the medium in which the waves are propagating. ...
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Why Klein-Gordon and Dirac's waves have a phase velocity of $c$?

From De Broglie’s relations and the energy-momentum dispersion relation one finds: $$v_p=\frac{w}{k}=\frac{E}{p}=\frac{\gamma mc^2}{\gamma mv}=\frac{c^2}{v} \tag{1}$$ Where, $v_p$ is the phase speed ...
physicsrev's user avatar
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Integration constants in geodesic equation for wave equation

I am stuck at a following "hello world problem". Let us consider the most common (d'Alembertian) wave equation: $$ \frac{\partial^2 \psi}{\partial^2 x} - \frac{1}{c_0^2}\frac{\partial^2 \psi}...
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Guided waves: showing geometrically that $v_p v_g = c^2$

In griffith's introduction to electrodynamics p.430 there's a Figure 9.25 of the wavefronts. I'm wondering if we can show geometrically $v_p v_g = c^2$ using this kind of figure. I think so, but I can'...
happypaticle's user avatar
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1 answer
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Shouldn't the velocity of the wave associated with a particle be equal to the velocity of the particle?

If a free particle of mass $m$ is moving with a velocity $v$, then it's kinetic energy is $\frac{mv^2}{2}$, therefore its frequency is $\nu = \frac{E}{h} = \frac{mv^2}{2h}$ where $h$ is Planck's ...
Anish Agrawal's user avatar
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Phase velocity definition and direction in Thorne/Blandford Optics

Following the book's very introduction to optics: Suppose we have a monochromatic wave described by $$\psi = A e^{i (\mathbf{k} \cdot \mathbf{x} - \omega t)} = A e^{i \varphi}.$$ The apparent ...
Petrini's user avatar
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2 answers
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Question regarding Group and Phase Velocity

https://youtu.be/EIqKG5TiSYs. I have some confusions regrading Group and Phase Velocity. Group Velocity exists for a group of waves, it's stated here in the video that Group Velocity the sum of the ...
Harry Case's user avatar
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1 answer
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De Broglie wave speed

I have a very introductory level in quantum mecanics and something remains unclear. Let $v$ be the speed of a particle (non-relativistic). From De Broglie, we have $p=h/\lambda$, where $\lambda$ is ...
Queta's user avatar
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Phase and group velocities in QFT / Quantum Optics

How does one define phase and group velocities in QFT? More precisely, are they referring to the mode structure of the field or do they characterize excitations? The question is motivated by question ...
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Speed of photon

Background: I originally asked this question Does a single photon propagate with phase velocity or front velocity through a dispersive material? about the speed of a single photon in a dispersive ...
Charles Tucker 3's user avatar
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Does a single photon propagate with phase velocity or front velocity through a dispersive material?

I know that we explain the slowing down of light in a dispersive medium classically, by inducing small dipoles in the medium (which holds as long as being far away from absorption bands), and the ...
Charles Tucker 3's user avatar
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1 answer
102 views

The phase velocity of a massive field is greater than $c$ [duplicate]

Assuming $c=1$, $v=\frac{\omega}{k}=\frac{\sqrt{k^2+m^2}}{k}>1$, for $m \neq 0$. Why is it not an issue that this $v$ is greater than the speed of light?
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Some confusion on group and phase velocity of a general wave group

While discussing a wave group, it has always been turned up as taking only two waves of different $k$ values, the resultant being a composition of a wave of larger $k$ modulated by an envelope of ...
som's user avatar
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1 answer
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Why is group velocity greater than phase velocity in glass?

I'm learning with Kenneth Krane Modern Physics 3ed. 28-(b) When white light travels through glass, the phase velocity of each wavelength depends on the wavelength. (This is the origin of dispersion ...
Pulsar's user avatar
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Free particle wavefunction has a carrier and envelope part

If $\psi(x, t)=\left(\frac{1}{2 \pi \alpha^{2}}\right)^{1 / 4} \frac{1}{\sqrt{\gamma}} e^{i p_{0}\left(x-p_{0} t / 2 m\right) / \hbar} e^{-\left(x-p_{0} t / m\right)^{2} / 4 \alpha^{2} \gamma}$ where ...
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Phase velocity of matter wave from the perspective of special relativity

I am a beginner of relativity. I read Relativity Made Relatively Easy by Andrew M. Steane. At chapter 6.4, p.118, he wrote about the phase velocity of matter wave in the viewpoint of relativity. I ...
Hsu Bill's user avatar
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3 answers
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How to calculate group and particle velocity given wave function?

Suppose you are given a wave function $\psi(x, t) = C\exp(i(kx - \omega t))$; how can you calculate the group and particle velocity? My intuition was to use group velocity: $v_g = \frac{\partial w}{\...
user572780's user avatar
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2 answers
345 views

Is the phase velocity infinite for a matter wave with group velocity zero?

The Wikipedia article on matter waves describes the dependency between phase velocity $v_p$ and group velocity $v$ as $$ v_p = \frac{c^2}{v} $$ So for group velocity $v=0$ the phase velocity is ...
Harald's user avatar
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Question regarding the intution behind Group and Phase velocity

I can't understand the proper idea behind Group and Phase Velocity. I don't get it as clearly as I would like. I want the intuition behind it. Phase velocity $v_p$ is given by $\frac{ω}{k}$, This ...
Harry Case's user avatar
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1 answer
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Is the ratio between phase velocity and group velocity a significant quantity?

Doing the ratio between phase velocity and group velocity for my specific application in the wavenumber domain I noticed that at a certain wavenumber the graph reaches a peak. Is the ratio between ...
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1 answer
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Relation between phase velocity and $\delta\omega$ and $\delta k$

I'm trying to find a relation between the phase velocity, $v_p=$$\omega \over k$ and $\delta\omega$ and $\delta k$, of a wave formed by adding the two waves: $$y_1=\cos(k_1 x-\omega_1 t)$$ and $$y_2=\...
Rohan Khatua's user avatar
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Phase velocity higher than the light speed for high frequencies in glass

The phase velocity is higher than the light speed for very high frequencies in glass, but nothing should transmit information faster than the light in the vacuum. So I read that a pure sinusoid wave ...
Redwaves's user avatar
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Dispersive media, imaginary velocity

In a dispersive medium we ave usually 2 dispersion laws: One that relates frequencies and Real Wavenumbers; One that relates frequencies and Imaginary Wavenumbers; With 1. I can find group and phase ...
Luca Mirtanini's user avatar
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1 answer
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Group - and phase velocity in communication via electromagnetic waves (radio)

I'd like to present the way I see group and phase velocities in the context of radio waves, and see whether or not my understanding is in some way flawed or lacking. I will summarize with a specific ...
In the blind's user avatar
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2 answers
478 views

Formula for phase velocity in dispersive medium

We know that phase velocity of a wave, $v_p=\frac{\omega}{k}$. For simple sinusoidal waves like - $y=a\sin(kx-\omega t)$. I can easily understand and prove this by simply setting $ kx-\omega t=c$ ($c$ ...
MD Hossain's user avatar
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2 answers
307 views

Velocity and frequency of general wave equation

How can we determine the velocity and frequency of a wave by only seeing it's equation. For example : If Given, $$y=A\cos(k_1x-w_1t)\sin(k_2x-w_2t)$$ an equation of a particular wave. Then what will ...
MD Hossain's user avatar
1 vote
2 answers
891 views

Phase velocity, Group velocity and group velocity dispersion (GVD)

I'm studying what happens to a wave packet if it propagates in a medium under linear optics conditions. In my equations I have the wave vector $k=\frac{\omega}{c}n(\omega)$ (often called $\beta$) ...
Tech's user avatar
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1 answer
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Contradicting answers for phase velocity and group velocity of light in a medium [closed]

The velocity of waves through the medium of refractive index $\mathrm{n}$ is $\sqrt{n / k}$. The group velocity in the medium is (a) $\frac{1}{3} V_{p}$ (b) $\frac{4}{3} V_{p}$ (c) $\frac{1}{2} V_{p}$ ...
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2 votes
1 answer
126 views

Question about superluminal group velocity from Schrödinger equation

According to the Schrödinger equation (SE) for a free particle, we have solutions of the form $Ae^{ikx} + Be^{-ikx}$. The wavenumber $k \in (-\infty, \infty)$. It is standard to point out that these ...
Wapiti's user avatar
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4 votes
1 answer
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Is there a general equation for the signal velocity?

The phase velocity is defined as $v_{ph} = \frac{w}{k}$ and the group velocity as $v_{g} = \frac{\partial w}{\partial k}$. Both can exceed $c$ in some situations. The velocity than can't exceed $c$ is ...
Denn's user avatar
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Where do the group and phase velocity terms come from in the wave function of the propagation of a dispersive wave packet?

I am reading Zettili's QM concepts and applications (second edition), and in section 1.8.3 where he discusses the motion of wave packets, we consider a wave packet where angular frequency $\omega$ is ...
Sceptual's user avatar
2 votes
1 answer
320 views

Phase and group velocity - deriving phase changes into animation

I have a question about the phase and group velocity topic. I am making an animation in Python showing both group and phase velocity changes. Let's assume we have 2 waves: $y_1 = A\cos(w_{1}t-k_{1}x)$ ...
norivotset's user avatar
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200 views

Why is the real part of the permittivity the phase angle?

The relative electric permittivity $\epsilon_r$ describes polarization inside a material due to electromagnetic waves (e.g., visible light passing a medium). I understand that the induced dipoles ...
Charles Tucker 3's user avatar
-1 votes
1 answer
797 views

Why phase velocity has no physical significance for a matter wave?

The following is quoted from my book: "The wavelength of a matter wave given by $λ= \frac{h}{p}$ has physical significance; its phase velocity $v_{p}$ has no physical significance. However, the ...
RIPAN BARUAH's user avatar
4 votes
4 answers
275 views

How do you visualize the particles in liquid at a molecular level?

I am studying about fluids at the moment and I never been so massively confused since about some fluid related topics that I thought I was confident about like liquid pressure, velocity of particles, ...
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Is the phase velocity of a matter wave equal to $c^2/v$, where $v$ is relativistic velocity? If so, what does that mean?

This is a result I accidentally derived while reviewing my notes from The Feynman Lectures on Physics, Vol I, Chapter 48 https://www.feynmanlectures.caltech.edu/I_48.html Begin with Feynman's eq. 48....
Steven Thomas Hatton's user avatar
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Huygens principle (phase velocity)

According to my physics book, the Huygens principle states that "given a wave front S at the instant of time t each point of this can be considered as a source of secondary spherical waves that ...
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1 answer
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How to convert the velocity field to a pressure field to information relating to sound level?

I am studying jet mixing noise and I am given a velocity field, with Vx, Vy, Vz in x and y coordinates. I wanted to know if there's a method in which I could find some information relating to the ...
fidafa123's user avatar
4 votes
1 answer
953 views

What is the mechanism of the Askaryan effect?

(Quoted largely from Wikipedia): Askaryan radiation, known otherwise as the Askaryan effect, is a phenomenon which occurs when a particle traveling faster than the phase velocity of light in a dense ...
10GeV's user avatar
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Is there a general relationship between the density operator and phase velocity?

I am trying to solve $\int v_pd\rho$ for a time-independent, 1-particle density operator $\rho$ (acquired, more or less, from a partial trace of complex scalar field operators projected upon the ...
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