Abstract: A model for acoustic transmission through a 2D square crystal of R-radius bubbles with\na lattice constant L was previously proposed. Assuming a purely monopole response of the bubbles,\nthis model offers a simple analytical expression of the transmission. However, it is not applicable\nwhen the bubbles are too close to each other (L/R < 5). This article proposes an extension of the model\nby including the dipole response of the bubbles. Comparisons with numerical and experimental\nresults show that the new expression gives a good estimate of the concentration at which the monopole\nmodel is no longer valid, but fails at properly predicting the transmission.
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