Purpose The purpose of this study is to investigate the complexities of two-dimensional deformations by employing the two-temperature nonlocal thermoelasticity theory. The research focuses on the coupling that occurs between mechanical waves, acoustic pressure, and the subsequent elastic material response. Understanding the ways in which the acoustic pres sure influences the thermoelastic and mechanical properties of materials is the primary focus of our trip. When it comes to the modification of the thermoelastic response during the declining heat source, we explicitly investigate the impact that acoustic pressure actually plays. Method In order to provide a narrative of the intertwined development of temperature and deformation fields in the vast canvas of two-dimensional (2D) space, theoretical formulations are constructed. Through the utilization of normal mode analysis (harmonic wave), we are able to successfully discover analytical solutions for the fundamental physical fields (wave propagation) of nonlocal physical fields. Results and Conclusion Particular boundary conditions are incorporated into our numerical simulations in order to improve their level of precision. The numerical results are subjected to a thorough theoretical analysis, and a colorful visual depiction of the path that the investigated physical quantities followed is provided in copper material