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Group vs phase velocity

What you are seeing: a two-component superposition. The orange dot tracks the carrier crest (phase velocity); the cyan dot tracks the envelope maximum (group velocity). For light, vg=vpv_g = v_p. For deep-water gravity waves, vg=vp/2v_g = v_p / 2 (the envelope moves slower than the crests). For the Schrödinger free-particle dispersion, vg=2vpv_g = 2 v_p.

Figure 1. Phase vs group velocity for several dispersion relations.
k_04.0
Δk0.50
dispersion

WHAT TO TRY

  • Vary each control and watch the rail readouts respond.
  • Compare the diagnostic plot against the live scene.