Impurities usually affect the transmission of acoustic signals, and how to effectively suppress their adverse effects is an important content in the research of acoustic materials. In a recent theoretical proposal, it was pointed out that perfect transmission through impurities can be achieved by adding a gain-loss distribution respecting parity-time ($\mathcal{PT}$) symmetry. In this paper, we demonstrate a similar but not identical way to realize the extraordinary physical property of impurity-shielding, which leads to perfect transmission at the so-called exceptional points. By systematically probing into the system composed of an equivalent medium slab sandwiched by a pair of $\mathcal{PT}$-symmetric metasurfaces, we obtain the two complementary solutions of exceptional points corresponding to perfect transmission. Interestingly, the two solutions of exceptional points coalesce into one when the mass density of the slab approaches zero. At such a critical point, we find that the impurity-shielding effect can be perfectly demonstrated, irrespective of embedded impurities of almost any shape and materials, whether they are Hermitian or non-Hermitian. In addition, the proposed system is frequency independent, indicating that the prototype can work well even in the subwavelength range. Our paper shows that exceptional points can be used to eliminate scattering of impurities in a density-near-zero medium, revealing their potential applications in acoustic sensing, directional imaging, and other related wave disciplines.
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