Acoustic Equation in a Lossy Medium
Mathematical Physics
2022-12-29 v1 math.MP
Abstract
Here, the acoustic equation for a lossy medium is derived from the first principle from the linearized compressible Navier-Stokes equation without Stokes' hypothesis. The dispersion relation of the governing equation is obtained, which exhibits both the dispersive and dissipative nature of the acoustic perturbations traveling in a lossy medium, depending upon the length scale. We specifically provide a theoretical cut-off wave number above which the acoustic equation represents a diffusive nature. Such a behavior has not been reported before, as per the knowledge of the authors.
Keywords
Cite
@article{arxiv.2212.13795,
title = {Acoustic Equation in a Lossy Medium},
author = {Tapan K. Sengupta and Prasannabalaji Sundaram and Aditi Sengupta},
journal= {arXiv preprint arXiv:2212.13795},
year = {2022}
}