Understanding Wave Dispersion & Group Velocity: Help Needed!

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Group velocity refers to the speed at which energy is transmitted through a group of waves. Dispersion in a medium occurs when the phase velocity of waves varies with frequency, affecting how different frequencies travel through the medium. A wave group, wave train, wave packet, and pulse are often used interchangeably, but they can have specific distinctions in certain contexts. Dispersive media respond to the frequency of waves, while non-dispersive media do not, leading to different propagation behaviors. The energy transfer in waves is associated with the effective wavefront, which moves at the group velocity.
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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