Wave Envelope

A simple demonstration of the distinction between a wave envelope and individual wave crests. The red curves depict the wave envelope, while the blue curve indicates the individual wave crests (in the context of a surface wave, the blue curve can be viewed as the water surface).

The blue curve is not propagating while the red curve is steadily propagating to the right, highlighting the distinction between the propagation of an individual wave crest.

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Derivation with KdV

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More Examples

Various Demonstrations of Wave Envelope vs. Wave Crest Propagation

Case	Continuous Wave Train	Solitary Wave
$c_{g}>c_{p}$: Envelope propagation faster than crest propagation.
$c_{g}=c_{p}$: Envelope propagation equal to crest propagation.
$c_{g}<c_{p}$: Envelope propagation slower than crest propagation.