# Group velocity Definition and 15 Discussions

The group velocity of a wave is the velocity with which the overall envelope shape of the wave's amplitudes—known as the modulation or envelope of the wave—propagates through space.
For example, if a stone is thrown into the middle of a very still pond, a circular pattern of waves with a quiescent center appears in the water, also known as a capillary wave. The expanding ring of waves is the wave group, within which one can discern individual waves that travel faster than the group as a whole. The amplitudes of the individual waves grow as they emerge from the trailing edge of the group and diminish as they approach the leading edge of the group.

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1. ### I Signals and group velocity

What exactly is a signal in wave physics? Is any wave considered a signal? Like, consider a superposition of harmonic plane waves, is the signals it carries considered the envelope(that travels at the group velocity) or the individual rippes that travel at a the phase velocity?
2. ### I Group velocity for an electromagnetic wave inside glass

Hi, I saw that the group velocity for an electromagnetic wave can be calculate with the following formula ##v_g = v_p + k \frac{d v_p}{dk}## Thus, since ##v_p = \frac{c}{n} = \frac{\omega}{k}## Is it correct to say that ##v_g = \frac{c}{n} + k(- \frac{\omega}{k^2})## where ##k =...
3. ### How to show speed is equal to group velocity?

Homework Statement My question is, how do I show that speed is equal to group velocity? More information at https://imgur.com/a/m6FwNaG Homework Equations v_g = dw/dk The Attempt at a Solution Part a is substitution, part b uses v_g = dw/dk, part c is multiplication by h-bar, but I am stuck...
4. W

### Group Velocity of Non-Dispersive Wave Packet

Homework Statement I know that for a dispersive wave packet, the group velocity equals the phase velocity, which is given by v=w/k. But how do I calculate the group velocity of a non-dispersive wave packet? I'm supposed to be giving an example with any functional form. Homework Equations...
5. ### I Dispersive medium as a field

I am studying phase and group velocity in non-dispersive and dispersive media. My question is the following: Is there any reason why a dispersive medium simply cannot be modeled as a type of field?
6. ### I Dispersion: expansion of wavenumber as function of omega

Hi! Dealing about wave propagation in a medium and dispersion, wavenumber k can be considered as a function of \omega (as done in Optics) or vice-versa (as maybe done more often in Quantum Mechanics). In the first case, k (\omega) \simeq k(\omega_0) + (\omega - \omega_0) \displaystyle \left...
7. ### Faster than Light... Superluminal Group Velocity

If general relativity in the formal sense constrains all velocities to the speed of light as a maximum, how would superluminal group velocities exceeding speeds of light (at their superpositions) be evaluated in mainstream physics? Would this be a case of General Relativity and Physics...
8. ### Group delay with Gaussian pulse

Hello! Starting from a gaussian waveform propagating in a dispersive medium, is it possible to obtain an expression for the waveform at a generic time t, when the dispersion is not negligible? I know that a generic gaussian pulse (considered as an envelope of a carrier at frequency k_c) can be...
9. ### Finding the Group Velocity for Shallow Water Wave

Homework Statement Find the group velocity for a shallow water wave: ##\nu = \sqrt{\frac{2\pi\gamma}{\rho\lambda^3}}## Homework Equations Phase velocity: ##v_p = \nu\lambda## group velocity: ##v_g = \frac{d\omega}{dk}## ##k=\frac{2\pi}{\lambda}## ##\omega = 2\pi \nu## The Attempt at a...
10. ### Simplifying square root

How is it equal to v in the end? I'm sorry for asking such questions. But I'm just trying to understand
11. ### Can someone give me a hand with large root here

i get the differentiation the halves cancel the 2 the h bar cancels the h bar square and to get rid of the root in the denominator the entire thing is squared But I cannot understand where the huge square root came from at the end where I circled. Can someone help me here
12. ### Group velocity definition

In the propagation of non-monochromatic waves, the group velocity is defined as v_g = \displaystyle \frac{d \omega}{d k} It seems here that \omega is considered a function of k and not viceversa. But in the presence of a signal source, like an antenna in the case of electro-magnetic wave or a...
13. ### Dispersion relation for non-relativistic quantum particles

In class I learn that we can get the dispersion relation for particles by using E=hbar*w and p=hbar*k. The calculated phase velocity is w/k = hbar*k/2m, while the group velocity is dw/dk=hbar*k/m. All these make sense to me, except one thing: I always thought that E=hbar*w=hf is only applicable...
14. ### Bandwidth Theorem

Homework Statement Consider a propagating wavepacket with initial length ## L_{0}##. Use the bandwidth theorem to show that the minimum range of angular frequencies present in the wavepacket is approximately: $$\Delta{\omega}\approx \frac{v_{g}}{L_{0}}$$ Homework Equations Bandwidth theorem...
15. ### Group velocity and information

What is the relationship between transmission of information and group velocity of a wave packet? I always keep hearing things like information always travels at the group velocity, it can't go faster than light etc. While I do understand (to an extent) about information not exceeding the...