Talk:Group velocity

message: The group velocity of a wave is the velocity with which the overall shape of the wave's amplitude (known as the envelope of the wave) propagates through space.
I have NO idea what this means! "overall shape of ...amplitude" ?  I thought amplitude was a number (scalar).  Even if its a vector, tensor or other function, the claim (implicit) that it has a "shape" which propagates is unhelpful gobble-de-gook.
What about talking about wave composition?  or "repeating units" (as in poly-"mers")
Amplitude is indeed a scalar, but is it not necessarily constant.  Consider shining a flashlight onto a wall.  The brightness is high inside some circle, but outside the circle it is low and eventually vanishes.  So if you were to plot the amplitude as a function of the position on the wall, it would look like some radially symmetric hill (high in the middle, low in the ends).  That is what people mean when they talk about shape, except that they are talking about the shape as a function of time rather than a function of wall position.  —Preceding unsigned comment added by 140.180.174.115 (talk) 14:11, 8 December 2007 (UTC)
replies: text: I think it should be "overall shape of ...amplitudes".--LungZeno (talk) 23:13, 18 January 2009 (UTC)
thread_title:  "overall shape of ...amplitude" 

message: The article here claims that:
For light, group velocity and phase velocity are related by the formula 
:v_g v_p = c^2 \,
where:
:vp is the phase velocity
:c is the speed of light in a vacuum.
but dispersion (optics) gives phase velocity:
:v = \frac{c}{n}
and group velocity
:v_g = c \left[ n - \lambda \frac{dn}{d\lambda} \right]^{-1}.
which imply that:
:v_p v_g = c^2 \left[ n (n - \lambda \frac{dn}{d\lambda}) \right]^{-1} \not= c^2.
Something is wrong here. i don't see why  \left[ n (n - \lambda \frac{dn}{d\lambda}) \right] 
should be equal to one. Boud 13:52, 13 September 2005 (UTC)
thread_title:  inconsistency with dispersion 

message: Leo-
:Can someone please post a picture or a trailer where the group velocity is different from the phase velocity, like how the travelling wave would look in the transverse point of view?
::Try http://krypton.mnsu.edu/~7364eb/Math113/groupvelocity.html  unsigned 
::: I tried to make a gif, but its a bit large. I think i need to cut out half the frames.. but i'm too lazy right now. Fresheneesz 03:34, 12 September 2006 (UTC)
thread_title: picture of group velocity

message: For whom feels inclined, I think a section on discussing the numerous experiments that claim "faster than light" but end up measuring group velocity is warranted.  It seems these keep cropping up.  Cburnett 00:28, 18 August 2007 (UTC)
thread_title:  "Faster than light" 

message: I think there should be a reference for the sentence: "Quantum mechanics has very accurately demonstrated this hypothesis, and the relation has been shown explicitly for particles as large as molecules." in the section "Matter wave group velocity", because this is quite a strong statement.  —Preceding unsigned comment added by Cholewa (talk • contribs) 13:42, 17 April 2008 (UTC)
thread_title:  Missing reference for measurement of group velocity of matter wave functions 

message: Great animation, eh?  —Preceding unsigned comment added by 202.7.183.131 (talk) 01:41, 6 October 2008 (UTC)
thread_title:  I love the animation 

message: The article lists some formulas for group velocity:
:
For light, the refractive index n, vacuum wavelength λ0, and wavelength in the medium λ, are related by
:\lambda_0=\frac{2\pi c}{\omega}, \;\; \lambda = \frac{2\pi}{k} = \frac{2\pi v_p}{\omega}, \;\; n=\frac{c}{v_p}=\frac{\lambda_0}{\lambda},
with vp = ω/k the phase velocity.
The group velocity, therefore, satisfies:
:v_g = \frac{c}{n + \omega \frac{\partial n}{\partial \omega}} = \frac{c}{n - \lambda_0 \frac{\partial n}{\partial \lambda_0}} = v_p \left( 1+\frac{\lambda}{n} \frac{\partial n}{\partial \lambda} \right) = v_p - \lambda \frac{\partial v_p}{\partial \lambda} = v_p + k \frac{\partial v_p}{\partial k}.
Maybe you think there is an error? Well, here is python 2 or 3 code that checks all of these:
from __future__ import division, print_function
from math import pi
c = 3e8
def w_of_k(k):
    return 5 + 6 * k + 7 * k**2 # a random function
def lam0_of_k(k):
    w = w_of_k(k)
    return 2*pi*c / w
def lam_of_k(k):
    return 2*pi / k
def vp_of_k(k):
    w = w_of_k(k)
    return w / k
def n_of_k(k):
    return c / vp_of_k(k)
k = 12.345 # a random value
w = w_of_k(k)
lam0 = lam0_of_k(k)
lam = lam_of_k(k)
vp = vp_of_k(k)
n = n_of_k(k)
dk = 1e-5
dw = w_of_k(k+dk) - w_of_k(k)
dlam0 = lam0_of_k(k+dk) - lam0_of_k(k)
dlam = lam_of_k(k+dk) - lam_of_k(k)
dvp = vp_of_k(k+dk) - vp_of_k(k)
dn = n_of_k(k+dk) - n_of_k(k)
print(dw / dk)
print(c / (n + w * (dn / dw)))
print(c / (n - lam0 * (dn / dlam0)))
print(vp * (1 + (lam / n) * (dn / dlam)))
print(vp - lam * (dvp / dlam))
print(vp + k * (dvp / dk))
This code will print the results of the six different formulas for vg. You can check for yourself that all six outputs approach the same limit (178.83 in this case) as dk gets smaller. If you change k, or if you change the dispersion formula, the six expressions will still all agree with each other -- I checked. (Of course I have checked the formulas analytically too, and I have checked them against references ... but I think this code above is the most fool-proof way to ensure that the formulas are free of typos.)
I hope that people do not change the formulas without double-checking them this way! --Steve (talk) 13:30, 26 September 2012 (UTC)
thread_title:  Formulas for group velocity 

message: We already have Group delay and phase delay; Group velocity and phase velocity for the same reasons. fgnievinski (talk) 17:18, 23 May 2016 (UTC)
replies: text: Looks very dangerous to me, but if you are prepared to do the Herculean task satisfactorily, try it on your sandbox page and invite editors there, to vet it. I have, and you must have, witnessed merging disasters, and they are really hard to avoid. As a rule, WP readers go for short, self-contained pithy answers, not in-depth expositions of things they are not inclined to read seriously about, e.g. in books. There is redundant reduplications of the connection between the two (phase/group) in the respective articles, but this is good, not bad, as it helps the reader who is too lazy or inflexible to read and appreciate both.  So, jamming more, rather than fewer, issues here would probably detract from the utility of the page, but of course, if you have gumption and time to do it, by all means, give it a try. Cuzkatzimhut (talk) 18:43, 23 May 2016 (UTC)
thread_title:  Merge 

message: A computer might be able to mathematically decompose the wave train into “individual wavelets of differing wavelengths traveling at different speeds,” but a person only discerns waves.  I will rewrite that part of the lede to reduce the dubious content. Constant314 (talk) 21:07, 22 April 2021 (UTC)
thread_title:  Expanding water waves in a pond