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.
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?
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 =...
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...
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...
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?
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...
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...
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...
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...
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
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...
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...
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...
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...