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When a wave, such as sound or light, scatters within a densely packedparticulate, it can be rescattered many times between the particles, which iscalled multiple scattering. Multiple scattering can be unavoidable when: tryingto use sound waves to measure a dense particulate, such as a composite withreinforcing fibers. Here we solve from first principles multiple scattering ofscalar waves, including acoustic, for any frequency from a set of 2D particlesconfined in a circular area. This case has not been solved yet, and itssolution is important to perform numerical validation, as particles within acylinder require only a finite number of particles to perform direct numericalsimulations. The method we use involves ensemble averaging over particleconfigurations, which leads us to deduce an effective T-matrix for the wholecylinder, which can be used to easily describe the scattering from any incidentwave. In the specific case when the particles are monopole scatters, theexpression of this effective T-matrix simplifies and reduces to the T-matrix ofa homogeneous cylinder with an effective wavenumber $k_\star$. To validate ourtheoretical predictions we develop an efficient Monte Carlo method and concludethat our theoretical predictions are highly accurate for a broad range offrequencies.

Effective T-matrix of a cylinder filled with a random 2 dimensional particulate