 Axial and arclength travelling-wave speeds

For a periodic inextensible filament with arclength period $\Lambda$ and projected axial period $\lambda$, material points slide tangentially through the wave frame at speed $Q$. An axial pattern speed $V$ relative to mean filament motion gives $Q\lambda /\Lambda =V$. Confusing the two speeds changes the swimming-to-wave-speed ratio by $\lambda /\Lambda$.