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We present experimental results on a model system for studying wavepropagation in a complex medium exhibiting low frequency resonances. Theseexperiments enable us to investigate a fundamental question that is relevantfor many materials, such as metamaterials, where low-frequency scatteringresonances strongly influence the effective medium properties. This questionconcerns the effect of correlations in the positions of the scatterers on thecoupling between their resonances, and hence on wave transport through themedium. To examine this question experimentally, we measure the effectivemedium wave number of acoustic waves in a sample made of bubbles embedded in anelastic matrix over a frequency range that includes the resonance frequency ofthe bubbles. The effective medium is highly dispersive, showing peaks in theattenuation and the phase velocity as functions of the frequency, which cannotbe accurately described using the Independent Scattering Approximation (ISA).This discrepancy may be explained by the effects of the positional correlationsof the scatterers, which we show to be dependent on the size of the scatterers.We propose a self-consistent approach for taking this "polydispersecorrelation" into account and show that our model better describes theexperimental results than the ISA.

Influence of positional correlations on the propagation of waves in a complex medium with polydisperse resonant scatterers