In this paper, we investigate the band gap and deaf bands in a two‑dimensional phononic crystal structure based on a boron nitride lattice. The results indicate that the band gap is highly dependent on the material properties, the contrast between the physical properties of the components and the substrate, and the structural geometry. We present a boron nitride structure with the following specifications: a lattice constant of 2.5 mm, radii of scatterers of r₁ = 0.4 mm and r₂ = 0.2 mm, along with the simulated band gap. For the structures under consideration, we examine the existence of deaf bands in the transmission spectrum along the ΓM direction. The mechanical wave output from the structure undergoes modifications compared to the input wave, influenced by the geometry and materials used. These modifications can yield useful information regarding material concentration and the acoustic properties of the compounds, aiding material identification. We investigate the energy band diagram and transmission spectrum for two material systems: a solid‑fluid structure (water and steel) and a fluid‑fluid structure (water and mercury). Simulations were performed using COMSOL Multiphysics software implementing the finite element method. This study demonstrates that the transmission spectrum provides more precise information than the band structure regarding mechanical wave transmission through the structure, as deaf bands identified in the band structure correspond to zero transmission.