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...