Aims: Null points are prominent magnetic field singularities in which the magnetic field strength strongly decreases in very small spatial scales. Around null points, predicted to be ubiquitous in the solar chromosphere and corona, the wave behavior changes considerably. Null points are also responsible for driving very energetic phenomena, and for contributing to chromospheric and coronal heating. In previous works we demonstrated that slow magneto-acoustic shock waves were generated in the chromosphere propagate through the null point, thereby producing a train of secondary shocks escaping along the field lines. A particular combination of the shock wave speeds generates waves at a frequency of 80 MHz. The present work aims to investigate this high frequency region around a coronal null point to give a plausible explanation to its generation at that particular frequency. Methods: We carried out a set of two-dimensional numerical simulations of wave propagation in the neighborhood of a null point located in the corona. We varied both the amplitude of the driver and the atmospheric properties to investigate the sensitivity of the high frequency waves to these parameters. Results: We demonstrate that the wave frequency is sensitive to the atmospheric parameters in the corona, but it is independent of the strength of the driver. Thus, the null point behaves as a resonant cavity generating waves at specific frequencies that depend on the background equilibrium model. Moreover, we conclude that the high frequency wave train generated at the null point is not necessarily a result of the interaction between the null point and a shock wave. This wave train can be also developed by the interaction between the null point and fast acoustic-like magneto-acoustic waves, that is, this interaction within the linear regime.