  Acoustic wave propagation in a fluid with a random assortment of identical
cylindrical scatterers is considered. While the leading order correction to the
effective wavenumber of the coherent wave is well established at dilute areal
density ($n_0 $) of scatterers, in this paper the higher order dependence of
the coherent wavenumber on $n_0$ is developed in several directions. Starting
from the quasi-crystalline approximation (QCA) a consistent method is described
for continuing the Linton and Martin formula, which is second order in $n_0$,
to higher orders. Explicit formulas are provided for corrections to the
effective wavenumber up to O$(n_0^4)$. Then, using the QCA theory as a basis,
generalized self consistent schemes are developed and compared with self
consistent schemes using other dynamic effective medium theories. It is shown
that the Linton and Martin formula provides a closed self-consistent scheme,
unlike some other approaches.
