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Fundamental features of rotationally symmetric acoustic cloaks withanisotropic inertia are derived. Two universal relations are found to connectthe radial and transverse phase speeds and the bulk modulus in the cloak.Perfect cloaking occurs only if the radial component of the density becomesinfinite at the cloak inner boundary, requiring an infinitely massive cloak. Apractical cloak of finite mass is defined in terms of its effective visibleradius, which vanishes for perfect cloaking. Significant cloaking is obtainedwhen the effective visible radius is subwavelength, reducing the totalscattering cross section, and may be achieved even as the interior radius ofthe cloak is large relative to the wavelength. Both 2D vs. 3D effects arecompared as we illustrate how the spatial dependence of the cloaking parameterseffect the total cross section.

Acoustic cloaking in 2D and 3D using finite mass