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Three-dimensional numerical simulations of magnetoacoustic wave propagationare performed in a sunspot atmosphere with a computational domain covering fromthe photosphere to the chromosphere. The wave source, with propertiesresembling the solar spectrum, is located at different distances from the axisof the sunspot for each simulation. These results are compared with the theoryof mode transformation and also with observational features. Simulations showthat the dominant oscillation frequency in the chromosphere decreases with theradial distance from the sunspot axis. The energy flux of the different wavemodes involved, including de Alfv\'en mode, is evaluated and discussed.

Mode transformation and frequency change with height in 3D numerical simulations of magneto-acoustic wave propagation in sunspots