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Here, the perturbation equation for a dissipative medium is derived from the first principle from the linearized compressible Navier-Stokes equation without Stokes's hypothesis. The dispersion relations of this generic governing equation are obtained for one and three-dimensional perturbations, which exhibit both the dispersive and dissipative nature of the perturbations traveling in a dissipative medium, depending upon the length scale. We specifically provide a theoretical cut-off wave number above which the perturbation equation represents diffusive and dissipative nature. Such behavior has not been reported before, as per the knowledge of the authors.