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Non-linear sound propagation is investigated computationally by simulating compressible time-developing mixing layers using the Large Eddy Simulation (LES) approach and solving the viscous Burgers Equation. The mixing layers are of convective Mach numbers of 0.4, 0.8 and 1.2. The LES results agree qualitatively with known flow behavior. Mach waves are observed in the near sound field of the supersonic mixing layer computed by the LES. These waves show steepening typical to non-linear propagation. Further calculations using the Burgers equation support this finding, where the initial wave slope has a role in kicking them. No visible non-linear propagation effects were found for the subsonic mixing layers. The effects of geometrical spreading and viscosity are also considered.