Questions tagged [phase-velocity]

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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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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 ...
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1answer
41 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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20 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\...
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2answers
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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
414 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
108 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
399 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
64 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
682 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
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: $$ \begin{align} v & = \frac{\omega}{k} \tag{1} \\[10px] v & = \sqrt{\frac{T}{u}} \tag{2} \end{align} $$ ...
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1answer
189 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
185 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
83 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
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 ...
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86 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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0answers
117 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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0answers
121 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
401 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
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'...
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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\...
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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
3k 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 ...
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1answer
649 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
716 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
335 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
454 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
731 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
740 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
10k 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
5k 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
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?
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3answers
778 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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820 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?
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38 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 guys suggest some books/online resources where I can ...
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1answer
504 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 ...
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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?
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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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1answer
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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 ...
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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 ...
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1answer
412 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 ...
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2answers
8k 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
865 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 ...
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1answer
523 views

Fermat principle: which index of refraction?

I am somewhat puzzled by a common formulation of the Fermat principle (light travel time), because it contains index of refraction related to phase velocity while light travel time through a slab of ...
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1answer
637 views

Why doesn't anomalous dispersion allow faster-than-light propagation?

It seems that the phase velocity of light could be greater than $c$, if $\sqrt{\epsilon \mu} < 1/c$, i.e. for anomalous dispersion. Are there examples of such media? For diamagnetics it seems ...
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6k views

In superluminal phase velocities, what is it that is traveling faster than light?

I understand that information cannot be transmitted at a velocity greater than speed of light. I think of this in terms of the radio broadcast: the station sends out carrier frequencies $\omega_c$ but ...
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3answers
17k views

How do you find the velocity function of a mechanical wave?

With the form $y(x,t)=A\sin(kx-\omega t+\phi_0)$, there are two variables, How do I find the velocity? I don't know I can apply derivative with two variables.