## 1 Introduction
The previous research on the development of acoustic metamaterials has shown promise in creating potential candidate structures to replace conventional acoustic filters. These metamaterials offer advantages over traditional filters in terms of tunability and manufacturability. From a tunability standpoint, previous studies have demonstrated that the acoustic bandgaps in these materials can be adjusted through topological modifications to attenuate specific frequency ranges. This highlights the versatility of acoustic metamaterials, as they can be easily customized to cater to different frequency requirements for noise attenuation. In contrast, conventional acoustic filters typically have a fixed frequency response and cannot be as easily modified or tuned to meet specific needs. From a manufacturing standpoint, acoustic periodic metamaterials offer the advantage of being easily produced using additive manufacturing methods like 3D printing [38], which avoids the toxic fabrication processes involved in conventional filters [39]. It is important to note that additive manufacturing machines are equipped with carbon filters, which help eliminate odors and volatile organic compounds during the printing process. This feature not only ensures a cleaner working environment, but also promotes better health for those involved in the operation. A fundamental step towards the design of metamaterials for noise attenuation involves obtaining the bandgaps. Despite the extensive work in the literature that examines various geometries [27; 28; 34; 35; 37], in terms of their efficiency for bandgap coverage and noise reduction, an important gap that has yet to be addressed is the lack of an extensive parametric analysis and further optimization. This work aims to fill this gap by first selecting some of the pre--existing 1D acoustic periodic metamaterial [28], and then implementing three geometric modifications to this geometry to create several new geometries, namely, Semi--Periodic, Tapered--Diverging, and Tapered--Converging, which are analyzed and further optimized for their bandgap coverage. The tapered geometries allow for a wider range of inlet--to--outlet ratios within a unit cell. The proposed comprehensive analysis involves considering a set of 505 design parameters used to find the bandgap using FE--[PERSON]'s theorem. The bandgap results were further normalized, a vital step to facilitate the utilization of a larger set of system parameters. The normalized bandgap results are then used along with a set of 401 various unit cell sizes, making a total of 202,505 study cases for this optimization across all geometries studied in this research. An important filtering process that involves excluding the geometries with high ratios of viscous thermal boundary layer thickness to the smallest diameter within the unit cell was applied. This is essential for ignoring entropy effects and focusingprimarily on the acoustic modes for the study and, therefore, the validity of the bandgap theorem. Finally, to verify the effectiveness of the optimal designs in attenuating noise within the audible frequency range, an external sound source was used for actuation at a given location and the acoustic sound pressure levels were found at several sensing locations to confirm the attained bandgaps. As a result, the optimal design identified in this work has shown significant bandgap coverage improvement over the desired audible frequency range compared to previous works [27; 28; 34; 35; 37].