Low- and high-frequency acoustic resonances are computed numerically via a high-order finite-element code for a generic two-dimensional high-lift configuration with a leading-edge slat. Zero mean flow is assumed, approximating the low-Mach-number situation at aircraft landing and approach. To avoid unphysical reflections at the boundaries of the truncated computational domain, perfectly matched layer absorbing boundary conditions are implemented in the form of the complex scaling method of atomic and molecular physics. It is shown that two types of resonance exist: resonances of surface waves which scale with the total airfoil length and longitudinal cavity-type resonances which scale with the slat cove length. Minima exist in the temporal decay rate which can be associated with the slat cove resonances and depend on the slat cove geometry. All resonances are damped owing to radiation losses. However, if coherent noise sources exist, as observed in low-Reynolds-number experiments, these sources can be enhanced acoustically by the above resonances if the source frequency is close to a resonant frequency.