Crest crossings through a dispersive wave packet ($N_{\mathrm{crossing}}=N_{\mathrm{snapshot}}{v}_p/v_g$)

For a nearly monochromatic packet of length $L$ travelling past a stationary observer, the snapshot count is $L/\lambda$ but the crossing count is $fL/v_g=(L/\lambda )(v_p/v_g)$. In the envelope frame the observer moves at $-v_g$ and the crests at $v_p-v_g$. For deep-water gravity waves, $v_p=2v_g$, so the observer counts twice as many crests as appear in an instantaneous snapshot. A sharply bounded monochromatic packet is an idealization; the count describes the approximately uniform central train.