Extracting improved mechanical properties such as high stiffness-high damping and high strength-high toughness are being investigated recently using high symmetry interlocking micro-structures. On the other hand, development of artificially engineered composite metamaterials has significantly widen the usability of such materials in multiple acoustic applications. However, investigation of elastic wave propagation through high symmetry micro-structures is still in trivial stage. In this work, a novel interlocking micro-architecture design which has been reported previously for the extraction of improved mechanical properties has been investigated to explore its acoustic responses. The finite element simulations are performed under dynamic wave propagation load at multiple scales of the geometry and for a range of material properties in frequency domain. The proposed composite structure has shown high symmetry which is uncommon in fiber-reinforced polymer composites and a desirable feature for isotropic behavior. The existence of multiple acoustic features such as band gap and near-isotropic behavior have been established. An exotic wave propagation feature, wave trapping and attenuation, has shown energy encapsulation in a series of repeating structures in a frequency range of 0.5 kHz to 2 kHz.