Phase Velocity
Definition
The speed at which a single wave crest moves — distinct from the speed of the overall pulse carrying the energy.
Symbol: · Unit: meter per second (m/s)
Technical definition
v_p = ω/k = λf. In dispersive media it differs from the group velocity; in waveguides it can exceed c.
Example
Ocean swell: new crests appear at the back of a wave group and race forward through it — crests move at phase velocity while the group advances at half that speed in deep water.
Common confusion
Students mix up phase and group velocity. Remember: crests move at phase velocity; the packet carrying the energy moves at group velocity.