Group velocity Definition and 123 Threads

I'm currently working with lasers and in relation to that, fiber optics. In the book I'm reading there's a section regarding modes and their "group velocity". The text claims that there is the following relation: v_g=v_p * sin(A) where v_g is the group velocity and...

how these two are related to each there? if refractive index is given as a function of angular frequency, how both are related? reflective index= omega*c / k.anyone?

Homework Statement we are given that an electron and a proton have the same KE.We are to compare their phase and group velocity... Homework Equations The Attempt at a Solution K=(γ₁-1)m₁c²=(γ₂-1)m₂c² Now, I found it very problematic to extract the ratio of v₁/v₂ in terms of...

Homework Statement "Use relativistic expressions for total energy and momentum to verify that the group velocity vg of a matter wave equals the velocity v of the associated particle." Homework Equations E^{2} = (pc)^{2} + (mc^{2})^{2} p = hbar * k E = hbar * \omega vg =...

As far as I can see, almost all the major textbooks on electrodynamics and nonrelativistic quantum mechanics make the following statement somewhere: The group velocity is (at least in lossless media) the speed of information propagation and it is always smaller than c. In the past I have...

I am wondering if group velocity can defined only for waves with very close wavenumber? I see a number of simulations which shows the superposition of two waves with slighlty different wavenumber and angular frequency, and a train of wave pulses is produced. The group velocity is then...

Is there any unconventional method to find out the relation between group velocity and phase velocity? know there is a method employing Fourier tarnsforms and another easier method as well

Homework Statement I do not know if it is a homework problem or not.The moderators will determine that.However,I read in acoustics books that it is a standard practice to use superposition of harmonic functions to denote a finite wave train, which cannot be given by a sine/cosine...

I’m currently taking a class in fluids in which we are studying different types of wave propagation. We discussed how for certain types of waves (such as deep-water ocean waves), the frequency (and phase speed) of each sinusoidal component is a functions of the wave number. This makes the...

Obtain the group velocity v_g and phase velocity v_p of 7.0 MeV protons/electrons. Write each answer as a multiple of the speed of light c. My work: 1. Finding the group velocity: v_g = \frac{\partial \omega}{\partial k} = \frac{\partial \left( E / \hbar \right)}{\partial \left( p /...

Hi, I'm trying to figure out what the group and phase velocities of a wave packet describing a particle are in the relativistic case. I started with the relationship between energy and impulse : E squared = p squared X c squared + rest mass squared X c to the fourth. In this, I input the...

The group velocity is always negative except k=0 and k=Pi/a in the optical mode, is there a reason from the general picture of crystal vibration? Well, it seems to me that optical mode describes the situation that different atoms in a unit cell have opposite motions. Also, in the optical...

Would someone be kind enough to please give physical meanings to these two terms? I have never fully understood their meaning and difference (although I know how to express them mathematically). If, say, I have a Gaussian-shaped signal in the frequency domain that I am sending through a...

I'm studying EM waves right now and I don't understand phase and group velocity very well. I know the definitions of phase and group velocity from here and what they look like from http://www.csupomona.edu/~ajm/materials/animations/packets.html . What I don't understand is why phase velocity...

For a superposition of two since waves of equal amplitude in a dispersive media, we find that the group velocity is given exactly by v_g = \frac{\omega_2-\omega_1}{k_2-k_1} and approximately by d\omega / dk|_{k=k_0}. How do we show that this approximation holds for any type of waves...

Dear Friends and Phorum, I need to know how to calculate the group velocity of light. I've read that's exactly "c", but I don't know how to calculate it.

Problem 9.22 from Griffiths: Show that in deep water (where the depth is greater than the wavelength) the wave velocity is twice that of the group velocity. where Vw = w/k and Vg = dw/dk where w is the angular frequency, and k is the wave number. I'm really not certain how to proceed...

I am kind of stuck in a question relating to phase velocity and group velocity. I have been given that the index of refraction of a media is inversely propotional to the vacuum wavelength. And we are supposed to show the group velocity is half the phase velocity. Now, the work I have done...

whats the differnce between phase and group velocity?? from what i understand (and this could be flawed) is that group velocity is the velocity of the wave packets being sent out by the object (or particle) and phase velocity is velocity of the wavepeaks which actually travel faster than the...

How do i go about verifying this statement: If the phase velocity is the same for all wavelenghts of a certain wave phenomenon (no dispersion), the group and phase velocities are equal. Do i just put the two formulas equal to each other and solve for something or what?

If a question says: The phase velocity of ripples on the liquid surface is (2πS / λp)^(1/2), where S is the surface tension and p is the density of the liquid. Find the group velocity of the ripples. I know that the phase velocity = omega/k, and group velocity = delta omega/delta k. Do I just...

What is group velocity? I have found a few small definitions, but for some reason I'm not quite understanding how it works. Here's one bit I have read: "Recent experimental evidence shows that it is possible for the group velocity of light to exceed c. One experiment made the group velocity...

Yi(x,t) = A*Sin(kix - {&omega}it), where i = 1, 2, 3 Phase velocity for two wave can be given by v = (&omega + [&omega]')/(k + k') and group velocity u = (&Omega - &omega')/(k - k') but what about three waves? I'm not sure what to do for three waves. I've looked all over my text and...