Two effective medium models for two-dimensional scalar wave propagation in random
inhomogeneous media are examined in a single theoretical framework. It is
shown how the hypotheses and self-consistency conditions in these models are
mathematically formulated. As a special case, a two-phase composite in
which circular cylindrical inclusions are embedded in a continuous matrix is
considered. Numerical calculations are performed for such composites with
different combinations of constituent properties in the frequency range up to
,
where geometric optic behavior starts appearing. The models mutually deviate
when the motion of inclusions is relatively large, such as at the resonance
scattering of the inclusions. Otherwise, deviations in the low-frequency regime
() are
negligible and those at high frequencies are also strikingly small. The same facts are
observed for two composites having very different constituent properties and in the
high-frequency limit.
Keywords
effective medium theory, wave propagation, composite
materials, multiple scattering
