Understanding Wave Dispersion & Group Velocity: Help Needed!

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SUMMARY

This discussion centers on the concepts of wave dispersion and group velocity, specifically how energy is transmitted through wave groups in dispersive media. It is established that in a dispersive medium, the phase velocity varies with frequency, leading to different propagation speeds for different wave components. The terms "wave group," "wave train," "wave packet," and "pulse" are confirmed to be synonymous. The effective energy transfer in waves occurs via the group velocity, which is crucial for understanding wave dynamics in various media.

PREREQUISITES
  • Understanding of wave mechanics and terminology
  • Knowledge of phase velocity and group velocity concepts
  • Familiarity with dispersive and non-dispersive media characteristics
  • Basic grasp of wave packets and their properties
NEXT STEPS
  • Research the mathematical formulation of wave dispersion in different media
  • Explore the relationship between phase velocity and frequency in dispersive media
  • Study the implications of group velocity on energy transfer in wave phenomena
  • Investigate real-world applications of wave packets in physics and engineering
USEFUL FOR

Students and professionals in physics, particularly those studying wave dynamics, as well as engineers working with wave propagation in various media.

samreen
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*for a group of waves, the energy is transmitted with the group velocity.
what does that mean?

*what is meant, as in actually meant, by dispersion of a wave in a medium? whatever i looked up says phase velocity depends on frequency for a dispersive medium and vice versa. Why?

* wave group=wave train of finite length=wave packet=pulse ? correct the wrong bits in this statement please

i need lots of help because I am in a soup here :(
 
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i think I've got it somewhat. a dispersive medium is one that can sense the discreteness of a complex wave. because frequency is an issue for it. whereas a non dispersive medium is too stupid to. for it, there effectively is just that fancy wave propagating thru it. and it isn't much bothered by the frequency. not an issue. unlike a dispersive medium, which reacts somehow to frquency, because the phase velocity is diff for diff frequencies.

and for any wave, the effective energy transfer may be assumed to be happening via the effective wavefront, which propagates with the effective velocity or group velocity. right so far??
 

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