In this work, we investigate non-Hermitian acoustic waveguides designed with periodically applied feedback efforts using electrodynamic actuators. One-dimensional spectral (infinite-dimensional) and finite element (finite-dimensional) models for plane acoustic waves in ducts are used. It is shown that dispersion diagrams of this family of metamaterials exhibit non-reciprocal imaginary frequency components, manifesting as wave attenuation or amplification along opposite directions for all pass bands. The effects of different feedback laws are investigated. Furthermore, the non-Hermitian skin effect manifesting as topological modes localized at the boundaries of finite domains is investigated and successfully predicted by the topology of the reciprocal space. This work extends previous numerical results obtained for a piezoelectric rod system and contributes to recent efforts in designing active metamaterials with novel properties associated with the physics of non-Hermitian systems, which may find fruitful technological applications related to noise control, wave localization, filtering and multiplexing.