Questions tagged [phase-velocity]

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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 ...
656 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 ...
126 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. ...
522 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? ...
71 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 ...
864 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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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} ...
217 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 ...
197 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, ...
85 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 ...
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 ...
92 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-...
123 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 ...
125 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 ...
443 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: $$\Psi(x,t) = \frac{1}{\sqrt{2 \pi}}\int_{-\infty}^{\infty} \phi(k)e^{ikx}e^{-\frac{i \hbar k^2 t}{2m}}dk.$$ ...
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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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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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 ...
414 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 ...
9k 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?