Higher Order Modes (HOMs) excited by the passage of the beam through an accelerating cavity depend on the properties of both the cavity and the beam. It is possible, therefore, to draw conclusions on the inner geometry of the cavities based on observations of the properties of the HOM spectrum. A data acquisition system based on two 20 GS/s, 6 GHz scopes has been set up at the FLASH facility, DESY, in order to measure a significant fraction of the HOM spectrum predicted to be generated by the TESLA cavities used for the acceleration of its beam. The HOMs from a particular cavity at FLASH were measured under a range of known beam conditions. The dipole modes have been identified in the data. The properties of these were compared with the results obtained from 3D simulations of a perfect cavity, as well as simulations of cavities with realistic imperfections, in order to ascertain the influence of geometry perturbations on the rf properties of the cavity.