Aero-acoustic simulations are performed for an orifice plate mounted in a straight duct in a low-Mach number flow. A two-dimensional flow-field is calculated by solv- ing the Navier-Stokes equations by means of a large-eddy simulation (LES), using a high-order finite difference scheme. The scheme uses summation-by-parts (SBP) finite difference operators with simultaneous approximation terms (SAT) to impose boundary conditions. The flow is decomposed using dynamic mode decomposition (DMD) in order to gain insight into the generation of sound by the flow. The frequency of the higher amplitude modes is shown to agree well the frequencies of the highest amplitude peaks in the power spectral density of the outgoing acoustic waves.