Rayleigh limits for effective wavenumbers of randomly distributed porous cylinders. Comparison of explicit and implicit methods

• Low concentrations of porous cylinders at low frequencies are considered.
• Wavenumbers from explicit and implicit formulas are compared.
• Effective mass densities and bulk moduli are given.

The effective wavenumber of the coherent wave propagating in a fluid containing parallel porous cylinders randomly distributed in space is derived at the Rayleigh limit for (i) explicit formulas: Independent Scattering Approximation (ISA), Waterman and Truell (WT) and Linton and Martin (LM) and (ii) for implicit formulas: Coherent Potential Approximation (CPA) and Generalized Self Consistent Method (GSCM) applied to WT and to LM. The effective mass density and bulk modulus are also derived. The validity of all the effective quantities is checked by recovering, when the porosity of the scatterers tends to zero, the case of an inhomogeneous medium of elastic cylinders.