Practical design of composite materials suggests a need for an improved quantitative understanding of the interaction between acoustic waves and microspheres. In this work, we first investigate the Mie resonance of a single spherical microsphere embedded in polymer by referring to the elements of the scattering matrices. It shows that a hollow glass microsphere presents a similar monopole resonance as an air microsphere, but the resonance of a hollow glass microsphere occurs at a higher frequency with a wider bandwidth than that of an air microsphere. Then, using the multiple scattering method, we show that the low-frequency gap of a periodic array of microspheres in polymer is mainly induced by the monopole resonance of the single microsphere, and find a wide band gap under very low concentrations of the microspheres. The viscosity of the components induces the energy dissipation under the resonant scattering, and the attenuation of ultrasonic longitudinal waves in the polymer slab is dominated by energy absorption.

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