  We consider the linear water-wave problem in a periodic channel which
consists of infinitely many identical containers connected with apertures of
width $\epsilon$. Motivated by applications to surface wave propagation
phenomena, we study the band-gap structure of the continuous spectrum. We show
that the for small apertures there exists a large number of gaps and also find
asymptotic formulas for the position of the gaps as $\epsilon \to 0$: the
endpoints are determined within corrections of order $\epsilon^{3/2}$. The
width of the first bands is shown to be $O(\epsilon)$. Finally, we give a
sufficient condition which guarantees that the spectral bands do not degenerate
into eigenvalues of infinite multiplicity.
