Sound Waves in a Medium with Resonance Inclusions of a Dipole Type

An elastic medium with inclusions that are small compared to the sound wavelength and differ in density is considered. If the inclusions are resonators that respond equally to the influence of waves coming from different directions, then the effective density of the medium in a certain frequency band becomes negative. If the direction of the dipole moment of the resonators is fixed, then the medium with inclusions has an anisotropic effective density. The Helmholtz equation for such a medium was obtained, and the field of a point source was studied.