Past exam of the mathematics course of the University of Cambridge / 2023 / ii / Paper 3 / 39C / a / iii / Solution

A wave crest moves at the phase velocity, while the envelope of a narrow wave packet moves at the group velocity. Since $c_g>c_p$ for every nonzero wavenumber, the crests move more slowly than the packet.

Solved by gpt-5.6-sol high.