Questions tagged [phase-velocity]
The phase-velocity tag has no usage guidance.
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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 ...
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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:
$$
\frac{\partial^2 \psi}{\partial^2 x} - \frac{1}{c_0^2}\frac{\partial^2 \psi}...
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Guided waves: showing geometrically that $v_p v_g = c^2$
In griffith's introduction to electrodynamics p.430 there's a Figure 9.25 of the wavefronts. I'm wondering if we can show geometrically $v_p v_g = c^2$ using this kind of figure. I think so, but I can'...
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Direction of the wave vector
The following paragraph from Wikipedia about phase/group velocity and direction of propagation is confusing me:
"The direction in which the wave vector points must be distinguished from the &...
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Shouldn't the velocity of the wave associated with a particle be equal to the velocity of the particle?
If a free particle of mass $m$ is moving with a velocity $v$, then it's kinetic energy is $\frac{mv^2}{2}$, therefore its frequency is $\nu = \frac{E}{h} = \frac{mv^2}{2h}$ where $h$ is Planck's ...
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Phase velocity definition and direction in Thorne/Blandford Optics
Following the book's very introduction to optics:
Suppose we have a monochromatic wave described by $$\psi = A e^{i (\mathbf{k} \cdot \mathbf{x} - \omega t)} = A e^{i \varphi}.$$
The apparent ...
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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 ...
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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 ...
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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 ...
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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 ...
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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 ...
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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 ...
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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 ...
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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}{\...
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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} $$
So for group velocity $v=0$ the phase velocity is ...
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Question regarding the intution behind Group and Phase velocity
I can't understand the proper idea behind Group and Phase Velocity.
I don't get it as clearly as I would like.
I want the intuition behind it.
Phase velocity $v_p$ is given by $\frac{ω}{k}$, This ...
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Is the ratio between phase velocity and group velocity a significant quantity?
Doing the ratio between phase velocity and group velocity for my specific application in the wavenumber domain I noticed that at a certain wavenumber the graph reaches a peak.
Is the ratio between ...
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Relation between phase velocity and $\delta\omega$ and $\delta k$
I'm trying to find a relation between the phase velocity, $v_p=$$\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 $$y_2=\...
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Phase velocity higher than the light speed for high frequencies in glass
The phase velocity is higher than the light speed for very high frequencies in glass, but nothing should transmit information faster than the light in the vacuum. So I read that a pure sinusoid wave ...
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Dispersive media, imaginary velocity
In a dispersive medium we ave usually 2 dispersion laws:
One that relates frequencies and Real Wavenumbers;
One that relates frequencies and Imaginary Wavenumbers;
With 1. I can find group and phase ...
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Group - and phase velocity in communication via electromagnetic waves (radio)
I'd like to present the way I see group and phase velocities in the context of radio waves, and see whether or not my understanding is in some way flawed or lacking. I will summarize with a specific ...
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Formula for phase velocity in dispersive medium
We know that phase velocity of a wave, $v_p=\frac{\omega}{k}$.
For simple sinusoidal waves like -
$y=a\sin(kx-\omega t)$.
I can easily understand and prove this by simply setting $ kx-\omega t=c$ ($c$ ...
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Velocity and frequency of general wave equation
How can we determine the velocity and frequency of a wave by only seeing it's equation. For example :
If Given,
$$y=A\cos(k_1x-w_1t)\sin(k_2x-w_2t)$$
an equation of a particular wave. Then what will ...
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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$) ...
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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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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 ...
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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 ...
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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 ...
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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)$ ...
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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 ...
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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 ...
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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....
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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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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 ...
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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 ...
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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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Definition of Phase Shifts (Coupled Oscillators)
I was wondering if maybe someone could look at this excerpt from a textbook (Attached). It states that “the displacement of the two masses will be in opposite directions (out of phase by pi)” but I ...
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Phase and group velocity calculation
I have a wave described by $A \sin(k_x x) \exp(i(k_y y− ωt))$. This wave is propagating in $+y$ direction. However its angular frequency is given by $k_x^2 + k_y^2 = (w/c)^2$. If I want to calculate ...
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Error in an argument for classical transverse Doppler effect
I was recently reviewing the classical Doppler effect for intro physics students. One aspect of such is that there's no transverse effect: An observer moving perpendicular to the motion of a plane ...
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Relationship between Phase Velocity and Velocity Factor
According to Wikipedia, the Velocity Factor, is the ratio of the speed at which a wavefront passes through a medium to the speed of light in a vacuum.
While the phase velocity is the rate at which a ...
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Theoretical question about waves and interference
Assume I’m given a standing wave function and I’m asked to find the phase velocity of the two waves that interfered and created the standing wave.
Now, I have two questions:
Is it possible to move ...
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Why is the speed of a quantum particle defined as coefficient of $t$ over coefficient of $x$?
I’m currently studying quantum mechanics from Introduction to Quantum Mechanics by Griffiths. In his free particle section, he says that the speed of a particle is the coefficient of $t$ over the ...
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Significance of Group velocity Equation
$$v_g\equiv\frac{\partial\omega}{\partial k}.$$
The above equation is for Group velocity of waves, so what is the Physical Interpretation of this Equation? As we know $k$ is wave number which shows ...
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Question concerning phase curves and Lissajous figures
I want to draw the "orbits" of a spherical pendulum under small oscillations. In this case its equations are given by $\ddot{x}_{1}=-x_{1}$ and $\ddot{x}_{2}=-x_{2}$. Of course the potential ...
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Is propagation speed depending of wavelength? (QM)
In case of a single free particle, no potential field, the wave function is:
$$ \Psi = A e^{i(kx-\omega t)}. $$
As it must fulfill the Schrödinger equation
$$ - \frac{\hbar^2}{2m} \nabla^2 \ \psi(\...
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