Membrane-guide phase and energy speeds ($v_{p,x}{v}_{g,x}=v^2$)

A fixed-edge membrane strip has dispersion ${\omega }_n^2=v^2[k_x^2+(n\pi /b{)}^2]$, n≥1. Differentiating gives $v_{g,x}=v^2{k}_x/{\omega }_n$, whereas $v_{p,x}={\omega }_n/k_x$. Their product is $v^2$. In this lossless scalar mode the integrated energy flux divided by energy density agrees with group speed. At cutoff the longitudinal group speed vanishes while formal phase speed diverges; an infinite phase speed therefore indicates no superfast energy transport.