Questions tagged [phase-velocity]

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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
43 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
34 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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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
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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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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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0answers
37 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
25 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
414 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
79 views

Why the direction of propagation of wave is perpendicular to wavefront at each point

Why is the direction of propagation of wave is perpendicular to wavefront at each point? I know this sounds intuitively true but a simple mathmatical proof would be very helpful. If i have an ...
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Link between properties of dispersive systems and group velocity larger than phase velocity

I recently bumped into systems where the group velocity is larger than the phase velocity (capillary waves for example). What does it mean in terms of system properties ? When does a system have a ...
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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{\...
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2answers
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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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1answer
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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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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
285 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
76 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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2answers
234 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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2answers
1k 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
225 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
896 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
88 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
1k 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
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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
284 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
257 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
91 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
66 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
128 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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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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138 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 ...
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139 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 ...
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1answer
533 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: $$\Psi(x,t) = \frac{1}{\sqrt{2 \pi}}\int_{-\infty}^{\infty} \phi(k)e^{ikx}e^{-\frac{i \hbar k^2 t}{2m}}dk.$$ ...
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1answer
3k 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'...
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3answers
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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\...
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1answer
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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 ...
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5answers
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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 ...
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1answer
898 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 ...
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3answers
881 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 ...
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1answer
425 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 $\epsilon$ (=$...
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1answer
621 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 ...
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2answers
898 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 $\omega / k$. ...
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4answers
766 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 ...
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1answer
12k 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 ...
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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 ...
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0answers
227 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?
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3answers
963 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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857 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 ...
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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?