  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.
