Questions tagged [phase-velocity]
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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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1answer
26 views
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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53 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 ...
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24 views
Group Velocity Clarification
There is something that confuses me a bit about how group velocity is sometimes introduced and explained. For example, Walter Lewin (great professor) in his lectures uploaded on youtube, explains the ...
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36 views
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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2answers
37 views
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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59 views
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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48 views
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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73 views
What is the definition of parallel phase speed for plane waves?
I am not sure about the definition of phase speed in more dimensions, in particular considering only parallel/perpendicular components of it.
I consider a plane wave, $\vec{E}_0e^{i(\vec{k}\cdot\vec{r}...
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29 views
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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45 views
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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1answer
47 views
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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49 views
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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31 views
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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1answer
33 views
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
$$ - \frac{\hbar^2}{2m} \nabla^2 \ \psi(\...
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1answer
31 views
Does self-phase modulation generate new frequency components?
Not a physicist. Hope to clarify some conceptual issues I have with non-linear propagation of light through a medium, since I seem to be mixing up some very fundamental concepts. Specifically, I am ...
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1answer
52 views
Phase velocity in monatomic chain
When considering a one-dimensional monatomic chain of atoms (identical masses $m$ & spring constant $\kappa$), one finds the following dispersion:
$$ \omega(k) = \sqrt\frac{\kappa}{m}\cdot\left|\...
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30 views
When height increases then why velocity becomes low?
It's an example.
The satellite is moving around the earth. But when its height increases its velocity becomes low
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46 views
How does the width or depth of a container of water affects the speed of an object (e.g. a toy boat) travelling on it?
How does the width or depth of a container of water affect the speed of an object (e.g. a toy boat) travelling on it?
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Lightspeed - what do we measure? Wave group, phase, front and signal velocities
I'm studying for an experiment of measuring the lightspeed c. It will be measured following the rotating mirrors method by Fizeau-Foucault, using a HeNe laser.
I could understand - and visualize - ...
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1answer
719 views
What is the correct expression for phase velocity of a relativistic free particle?
According to most books,the relativistic free particle with velocity $v$ has phase velocity, $$v_p=\frac{c^2}{v}\tag{1}$$
But, a free particle also means potential energy $V=0$.Therefore we might as ...
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1answer
70 views
Phase velocity of a wave function across a potential energy step
I'm trying to do point c of problem 2.34 in Griffiths' book on QM:
It requires that I find the relative phase speed of the wave function outside and inside the potential. We're given the expression ...
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36 views
What is the difference, if any, between propagation velocity and phase velocity?
My textbook for my electromagnetic waves class mentions both propagation velocity and phase velocity separately, without specifically defining either. When I googled both terms, I couldn't find a ...
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1answer
130 views
Does phase velocity or group velocity change when light enters a new material? Contradictory sources
I'm so confused. I've read in this book (page 28) that group velocity of light can exceed $c$ in certain gases. However a lot of people online and in the forums say that phase velocity can exceed $c$.
...
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34 views
Why do matter waves have superluminal phase velocites?
Specifically why do they have $V = \frac{c}{β}$ as stated in this paper written by De Broglie: http://aflb.ensmp.fr/LDB-oeuvres/De_Broglie_Kracklauer.pdf ?
I follow the proof of “phase harmony” ...
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40 views
Which formulae should I use when calculating the frequency of an electron given its speed? [duplicate]
If I know the speed of an electron, how should I go about calculating its frequency?
For example, if the electron was travelling at $v$ $ms^{-1}$ there are two options I could take.
Calculate the ...
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1answer
45 views
What are the phase speeds of $A_0$ and $S_0$ Lamb waves at very low frequencies?
Lamb waves are elastic wave modes in plates. In general, they are mathematically complex to deal with, and numerical solutions are typically used to find dispersion curves for each mode, as shown in ...
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3answers
2k views
How to calculate the phase and group velocity of a superposition of sine waves with different speed and wavelength?
This might seem like a trivial question but it is not for me. So, I was reading on group and phase velocities from A.P. French where he calculates the phase and group velocities for a superposition of ...
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1answer
346 views
Why the direction of propagation of wave is perpendicular to wavefront at each point
Why is the direction of propagation of a wave perpendicular to the wavefront at each point? I know this sounds intuitively true, but a simple mathematical proof would be very helpful.
If I have an ...
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62 views
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
$$ v= \frac{\...
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3answers
293 views
Is the group velocity times the phase velocity always the velocity of light squared?
Can there be cases where it is different from $c$ squared? If so in what situations would it differ?
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346 views
Seeming violation-wave travelling faster than speed of light
Consider the basic relation $$E=\sqrt{(pc)^2+(mc^2)^2}.$$
Every particle possesses a wave nature and it depends on the situation in which one among the two is perceptible...
Consider a particle with ...
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67 views
Wave packet - phase vs group velocity
So, I've been revising QM recently and the concept of group vs phase velocity has me confused.
Let's say we have a wave packet. As quoted in Griffiths, "...A wave packet is a superposition of ...
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2answers
807 views
What does phase velocity physically represent, and why can it be superluminal? [duplicate]
Phase velocity is defined as $v_p=\frac{\omega}{k}$ and is described in various textbooks as being the speed at which the phase of a wave propagates. If you have a wave train that is modulated by an ...
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1answer
137 views
Wave packet in dispersive medium, how will the group velocity be affected? [closed]
A wave packet with center frequency ω is propagating in dispersive medium with phase velocity of 1.5 x 10^3 m/s. When the frequency ω is increased by 2%, the phase velocity is found to decrease by 3%. ...
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351 views
What really is the speed of light in a medium/vacuum, group or phase velocity?
While reading about refractive index 2 terms popped up, group velocity which alway slows down in a medium and phase velocity which may exceed speed of light. Say in a complete vacuum and using laser ...
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2k views
Phase Velocity Derivation
I spend few hours trying to derive phase velocity of sinusoidal wave $$\cos(kx - \omega t).$$ I know that it must be equal to $\omega \over k$ but after banging my head for few hours and trying to ...
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2answers
359 views
Why we do not use $v=f \lambda$ for the waves associated with particles?
As the waves travel with velocity $$v= f \lambda,$$ where $v$ is velocity, $f$ is frequency and $\lambda$ is wavelength. Here we can see that velocity of wave is directly proportional to wavelength. ...
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2answers
1k views
Wave group and phase velocities
When talking about phase velocity and group velocity they tend to be both expressed in terms of another $v$. From my understanding this $v$ comes from the wave equation, but what does it represent? ...
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1answer
113 views
Why is refractive index equals to speed of light upon phase velocity and not group velocity?
We have been using group velocity for most purposes as its the velocity with which the wave packet travels, they why do we use phase velocity for calculating refractive index.
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How is the phase velocity for a wave in a stringed instrument derived?
I was searching on the internet for a formula relating velocity of wave and force of tension of a string (eg how the tension in a string instrument effects the velocity) and this formula keeps ...
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1answer
2k views
Why the relationship $v_p v_g = c^2$ (phase velocity multiply group velocity equals lightspeed squared) exists in waveguide structures?
What’s the reason that the relationship of de Broglie hypothesis(hypothesis-->relations) will hold in Waveguide structures?
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1answer
8k views
Are these definitions for transverse wave velocity on a string consistent?
I've found two definitions for the velocity of a transverse wave on a stretched string:
$$
\begin{align}
v & = \frac{\omega}{k} \tag{1} \\[10px]
v & = \sqrt{\frac{T}{u}} \tag{2}
\end{align}
$$
...
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1answer
501 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 ...
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1answer
300 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, ...
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2answers
95 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 ...
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1answer
70 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 ...
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1answer
146 views
What is the phase velocity of light in graphene?
This article states that light can "slow down by a factor of a few hundred" when it strikes graphene. I've read elsewhere that the index of refraction of graphene is about 2.65 + 1.27i. According to ...
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97 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-...
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156 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 ...
