Abstract
An effective medium theory has been developed to study the viscous absorption of a doubly periodic phononic crystal, here denominated as supercrystal (SC). In practice, the SC is made of hard cylindrical scatterers embedded in a viscous fluid and consists of a combination of two phononic crystals with lattice periods, $a_1$ and $a_2$. The decay coefficient of sound due to viscosity is calculated analytically at low frequencies when both lattices homogenize. The viscous absorbance of finite SC slabs calculated with the analytical model is supported by exact calculations based on the finite element method (COMSOL simulations). In addition, results for the complex sound speed show a good agreement with the experimentally extracted sound speed.
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