Application of differential equation in the field of acoustic

The current study examines a classification of physical problems involving the attenuation and propagation of structure and fluid-coupled acoustic waves in a discontinuous waveguide. In acoustics, the response of sound to boundaries is important. Therefore, it is expected that all of the discontinuous waveguide’s boundaries have the same walls, which can be either hard or impedance. The impedance and hard walls of the waveguide are mathematically modeled with respective Robin and Neumann boundary conditions together with the second-order field differential equation. The physical challenge is solved using the mode-matching (MM) approach, which also matches the continuity criteria for the acoustic pressure and normal velocities at matching connections. Transmission loss and powers scattering graphs against various frequencies and waveguides dimension parameters are shown to evaluate how well the waveguide predicts the sound to enhance or attenuate for both fluid and structure-borne modes incidents. By reconstructing the matching continuity requirements at matching junctions and using the conserved power identity, the accuracy of the derived algebra is confirmed. The current study has significant implications for improving sound quality for audible applications.