I am working thru a derivation of the group velocity formula and I get to this stage: y=2Acos(xΔK2−tΔω2)sin(ˉkx−ˉωt)
Then all the derivations I have seen say that ΔωΔK is the group velocity. I know mathematically why this is a velocity but what I don't get is why do we know that this is the group velocity rather then the phase velocity and that ˉωˉk is the phase velocity and not the group velocity?
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