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

Multiple scattering by cylinders immersed in fluid: high order approximations for the effective wavenumbers