 Equal-phase two-wave membrane modes

Two equal complex amplitudes with opposite transverse wavevector components sum to a cosine across a strip with edges $y=\pm a/2$. Identical phases satisfy the edge condition only for the odd transverse indices displayed. Equal magnitudes with opposite phase give the sine family; together the families form all Dirichlet strip modes $n\pi /a$, $n\ge 1$. The lowest axial phase velocity exceeds the unrestricted membrane wave speed, while its group velocity is smaller; neither should be substituted for the other.