Reciprocity is a fundamental property related to T-symmetry of wave equation. Nonreciprocal acoustic transmission becomes possible in a nonlinear or in a moving medium. Viscous losses, which break T-symmetry, are not considered as a nonreciprocal factor. We demonstrate that transmission through a finite-length dissipative phononic crystal is nonreciprocal for asymmetric scatterers. Asymmetric transmission is known even for inviscid background. However, additional nonreciprocal contribution related to the vorticity mode is usually missing. For infinite dissipative phononic crystal we prove that the decay coefficients turn out to be equal for the opposite directions but the velocity remains nonreciprocal due to broken PT-symmetry.
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