  We present experimental results on a model system for studying wave
propagation in a complex medium exhibiting low frequency resonances. These
experiments enable us to investigate a fundamental question that is relevant
for many materials, such as metamaterials, where low-frequency scattering
resonances strongly influence the effective medium properties. This question
concerns the effect of correlations in the positions of the scatterers on the
coupling between their resonances, and hence on wave transport through the
medium. To examine this question experimentally, we measure the effective
medium wave number of acoustic waves in a sample made of bubbles embedded in an
elastic matrix over a frequency range that includes the resonance frequency of
the bubbles. The effective medium is highly dispersive, showing peaks in the
attenuation and the phase velocity as functions of the frequency, which cannot
be accurately described using the Independent Scattering Approximation (ISA).
This discrepancy may be explained by the effects of the positional correlations
of the scatterers, which we show to be dependent on the size of the scatterers.
We propose a self-consistent approach for taking this "polydisperse
correlation" into account and show that our model better describes the
experimental results than the ISA.
