Group Velocity Derivation: Understanding the Role of Ignored Terms

In summary, group velocity is a concept in wave mechanics that refers to the speed at which the overall shape or envelope of a wave packet propagates through a medium. It is different from phase velocity, which only takes into account the speed of individual wave crests or troughs. The mathematical derivation of group velocity involves using the wave equation and taking the derivative with respect to time. Group velocity is significant in understanding wave behavior in different mediums and has practical applications in optics, telecommunications, and quantum mechanics.
  • #1
chingel
307
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
  • #2
Group velocity cares about the speed of the amplitude, phases are not relevant for the group velocity.
 
  • #3
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?
 

Related to Group Velocity Derivation: Understanding the Role of Ignored Terms

What is group velocity?

Group velocity is a concept in wave mechanics that refers to the speed at which the overall shape or envelope of a wave packet (a group of waves) propagates through a medium.

How is group velocity different from phase velocity?

Group velocity is different from phase velocity in that it takes into account the speed at which the overall shape or envelope of a wave packet travels, while phase velocity refers to the speed at which an individual wave crest or trough travels through a medium.

What is the mathematical derivation of group velocity?

The mathematical derivation of group velocity involves using the wave equation, which describes the relationship between the frequency, wavelength, and speed of a wave, and taking the derivative with respect to time. This results in an equation for group velocity that takes into account the dispersion of the wave packet.

What is the significance of group velocity in wave mechanics?

Group velocity is significant because it helps us understand how wave packets behave in different mediums. It can also help us predict the behavior of waves in complex systems, such as in optics or quantum mechanics.

How is group velocity used in practical applications?

Group velocity is used in a variety of practical applications, including in optics for designing lenses and other optical devices, in telecommunications for signal transmission, and in quantum mechanics for understanding the behavior of particles at the quantum level.

Similar threads

Group velocity and phase velocity
    • Mechanics
Replies
4
Views
1K
Can anybody help with group velocity simulations?
    • Mechanics
Replies
18
Views
4K
Group velocity of a wavepacket vs its mean phase velocity
    • Mechanics
Replies
3
Views
1K
Understanding the Concept of Phase Velocity: Explained Simply
    • Mechanics
Replies
4
Views
1K
I Speed of light after exiting a transparent medium
    • Special and General Relativity
Replies
17
Views
714
Group Velocity of Non-Dispersive Wave Packet
    • Introductory Physics Homework Help
Replies
3
Views
1K
I Phase velocity and frequency of a matter wave
    • Quantum Interpretations and Foundations
2
Replies
41
Views
4K
I What does the wavenumber in a group velocity represent?
    • Atomic and Condensed Matter
Replies
2
Views
2K
What is phase velocity and how does it relate to group velocity?
    • Mechanics
Replies
6
Views
4K
What's the truth about phase velocity vs. group velocity?
    • Mechanics
Replies
4
Views
6K

Hot Threads

Recent Insights

Back
Top