  The lack of observed sausage perturbations in solar active region loops is
customarily attributed to the relevance of cutoff axial wavenumbers and the
consequent absence of trapped modes (called ``evanescent eigenmodes'' here).
However, some recent eigenvalue problem studies yield that cutoff wavenumbers
may disappear for those equilibria where the external density varies
sufficiently slowly, thereby casting doubt on the rarity of candidate sausage
perturbations. We examine the responses of straight, transversely structured,
coronal slabs to small-amplitude sausage-type perturbations that excite axial
fundamentals by solving the pertinent initial value problem with eigensolutions
for a closed domain. The density variation in the slab exterior is dictated by
some steepness parameter $\mu$, and cutoff wavenumbers are theoretically
expected to be present (absent) when $\mu \ge 2$ ($\mu < 2$). However, our
numerical results show no qualitative difference in the system evolution when
$\mu$ varies, despite the differences in the modal behavior. Only oscillatory
eigenmodes are permitted when $\mu \ge 2$. Our discrete eigenspectrum becomes
increasingly closely spaced when the domain broadens, and an oscillatory
continuum results for a truly open system. Oscillatory eigenmodes remain
allowed and dominate the system evolution when $\mu <2$. We show that the
irrelevance of cutoff wavenumbers does not mean that all fast waves are
evanescent. Rather, it means that an increasing number of evanescent eigenmodes
emerge when the domain size increases. We conclude that sausage perturbations
remain difficult to detect even for the waveguide formulated here.
