In the study of acoustic metamaterials, these artificial devices possess the ability to manipulate elastic wave propagation through alterations, deflections, blocks, or amplifications. This research focuses on the blocking characteristics of wave propagation, aiming to derive the associated Floquet-Bloch spectra, which establish the relationship between frequencies and wavelengths. The examination of the frequency band structure allows the determination of whether the device functions as a metafilter. Such behavior becomes evident when frequency band structures reveal band gaps. The primary objective is to manipulate these band gaps through active control, facilitating the adjustment of filter behavior across various selectable frequency ranges. Building on the work of Bacigalupo et al. and Lu et al., a novel electrically active acoustic metamaterial has been created to control the propagation of elastic waves. This involves integrating shunted piezoelectric inertial resonators into the periodic metamaterial with hexagonal blocks and elastic interfaces proposed by Bacigalupo and Gambarotta. The shunted piezoelectric resonator serves as the active component of the device. By tuning the impedance/admittance of a shunt circuit in parallel with the resonators, it becomes possible to modify the constitutive properties of this component and, consequently, tune the acoustic response of the entire device. This tuning process involves opening or closing band gaps in the associated Floquet-Bloch spectra. To validate these findings, numerical experimental tests are conducted, aiming to determine the device's capability to prevent wave propagation under specific conditions and to assess the effectiveness of active control.