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We provide the rst classical derivation of the Lloyd{Berry formula for the eectiv e wavenumber of an acoustic medium lled with a sparse random array of identical small scatterers. Our approach claries the assumptions under which the Lloyd{Berry formula is valid. More precisely, we derive an expression for the eectiv e wavenumber which assumes the validity of Lax's quasi- crystalline approximation but makes no further assumptions about scatterer size, and then we show that the Lloyd{Berry formula is obtained in the limit as the scatterer size tends to zero.

Multiple Scattering by Multiple Spheres: A New Proof of the Lloyd--Berry Formula for the Effective Wavenumber