In the literature, the coupled wavenumbers in flexible-walled acoustic waveguides have been found mainly using numerical methods for a fixed set of parameters. These solutions, although useful, do not continuously track the coupled wavenumbers as the fluid-loading parameter is varied from small to large values. Such a continuous tracking is possible by applying the asymptotic methods to the coupled dispersion relation. Analytical formulae for the coupled wavenumbers can also be found. In this work, we present a consistent, unified and physically insightful view of structural acoustic coupling in the context of a planar structural-acoustic waveguide (with two different BCs), the axisymmetric and beam modes of a fluid-filled circular cylindrical shell and finally a fluid-filled elliptic cylindrical shell. In all the five cases, we use a single fluid-structure-coupling asymptotic parameter (μ). The regular perturbation method is used to solve the coupled dispersion relation for small and large values of μ. The circular and the elliptic cylinders necessitate the use of additional asymptotic parameters. A general trend in all systems is that a given wavenumber branch transits from a rigid-walled solution to a pressure-release solution with increasing μ. Also, the wavenumber curves veer where the earlier uncoupled wavenumbers intersected.