Group Velocity Derivation: Understanding the Role of Ignored Terms

Click For Summary
SUMMARY

The discussion centers on the derivation of group velocity as presented on Wikipedia. It clarifies that the terms ignored before the integral sign do not affect the group velocity calculation because they pertain to phase shifts rather than amplitude propagation. The key takeaway is that group velocity specifically measures the speed of wave packet amplitudes, making phase terms irrelevant in this context. The participants emphasize the importance of distinguishing between amplitude and phase when analyzing wave behavior.

PREREQUISITES
  • Understanding of wave mechanics and wave propagation
  • Familiarity with the concept of group velocity
  • Basic knowledge of calculus, particularly integrals
  • Experience with mathematical physics terminology
NEXT STEPS
  • Study the mathematical derivation of group velocity from first principles
  • Explore the implications of phase velocity versus group velocity in wave theory
  • Investigate applications of group velocity in optics and telecommunications
  • Learn about the role of dispersion in wave propagation
USEFUL FOR

Physics students, wave mechanics researchers, and professionals in telecommunications seeking to deepen their understanding of wave behavior and group velocity calculations.

chingel
Messages
307
Reaction score
23
I was reading the derivation on Wikipedia:

http://en.wikipedia.org/wiki/Group_velocity#Derivation

Why is the first part before the integral sign ignored when calculating the velocity? Surely it would also cause a phase shift in some time interval and make the waves move forward (or backward)?
 
Physics news on Phys.org
Group velocity cares about the speed of the amplitude, phases are not relevant for the group velocity.
 
Ok, but when calculating the velocity by dividing the terms in front of t by those in front of k, why can some of the terms in front of t be ignored?
 

Similar threads

Graduate Can anybody help with group velocity simulations?
  • · Replies 18 ·
Replies
18
Views
6K
Graduate Understanding the Concept of Phase Velocity: Explained Simply
  • · Replies 4 ·
Replies
4
Views
2K
Graduate What's the truth about phase velocity vs. group velocity?
  • · Replies 3 ·
Replies
3
Views
7K
Undergrad Deriving the time-dependent wave equation from Energy eigenfunctions
  • · Replies 1 ·
Replies
1
Views
2K
Graduate Group, phase and signal velocity of light
  • · Replies 2 ·
Replies
2
Views
2K
Undergrad Non-locality by memory (Jung, 2020) applied to stochastic mechanics
  • · Replies 5 ·
Replies
5
Views
2K
Graduate Group velocity at Brillouin zone boundary
  • · Replies 1 ·
Replies
1
Views
10K
Undergrad The wave equation interpretation of special relativity
  • · Replies 10 ·
Replies
10
Views
1K
Group/Phase velocity - amplitude, frequency, velocity
  • · Replies 1 ·
Replies
1
Views
3K
Graduate General equation for hyperbolic motion in a 2D plane -- Help needed please
  • · Replies 14 ·
Replies
14
Views
2K