Propagation of low frequency acoustic waves in periodic 2D-lattices of tubes

Abstract

The problem of an acoustic, 2D-lattice of tubes is investigated. A “ladder” lattice is analyzed as a superposition of two 1D-lattices, symmetrical and antisymmetrical, respectively. Then infinite, complete 2D-lattices are analyzed by using the Green function method adapted from solid state physics. In the far field produced by a point source, the energy flux vector is found to have a radial direction, but not the wavevector, except on the main axes. In the horizontal or vertical directions, one finds from a recurrence relation a superposition of two waves (one is evanescent, and the other one is propagating or evanescent). Then a numerical computation of a finite lattice allows one to analyze the reflections on the boundaries. Finally, the agreement between experimental results on a small lattice and numerical results is found to be satisfactory.