In this work we investigate a periodic structure in the frequency range from 20 Hz to 5500 Hz designed for broadband noise insulation. The considered unit cell consists of a simple structure: a pair of polymer pipes with slits carved along the axes, representing two coupled Helmholtz resonators. In order to develop a design with a broad band gap, we analyze the eigenmodes of the infinite two-dimensional structure considering their symmetry and interaction. This analysis is supported by parametric optimization of the resonator geometry. The obtained band diagram is compared with numerically determined transmission coefficient of a finite structure based on the same unit cell. The number of unit cells of the finite structure is chosen to be sufficient for demonstration of insulating properties and stop band formation. Furthermore, we analyze how the transmission coefficient is linked to the pressure field distribution inside the resonators. Owing to the simplicity of the geometry, the obtained results may become a basis for development of budget-friendly passive systems for broadband noise insulation within the audible range of frequencies.