Upward refraction of sound propagating outdoors by a graded index sonic crystal noise barrier

Upward refraction of sound propagating outdoors by a finite set of two-dimensional cylinders has been studied in the homogenization region. All cylinders in the field are located above a ground plane and have their longitudinal axes orientated parallel to the ground. By increasing the cylinder radius with height, a graded index medium is created whose effective sound speed decreases over height. A cylindrical wave propagating inside a structure obeying such properties can be refracted upwards, consequently creating a zone of reduced pressure behind it. Acoustic phenomena for continuous graded index media (GRIN CM), predicted using the Finite Element Method (FEM), are demonstrated. Using modified homogenization formulas the results are then matched with a qualitatively equivalent graded index sonic crystal (GRIN SC), predicted with Multiple Scattering Theory (MST). It is shown that GRIN SC noise barriers potentially can be effective as broadband noise mitigation measures, with a barrier setup filling a cross sectional area not bigger than two meter squared. However, in order to gain a reasonable insertion loss, the barrier thickness must be chosen in accordance with the wavelength of the incoming field and should be in the order of a few wavelengths. Furthermore, the performance of these refractive structures is determined by the shape of the effective sound speed profile in relation to the point of excitation.