The wave finite element method has previously been used to understand the various types of wave in a passive cochlear model. In this paper, the model is extended to give an initial representation of an active cochlea by making the real and imaginary components of the Young's modulus, that defines the local dynamics of the plates representing the basilar membrane, position and frequency dependent. At a given excitation frequency, the distribution of the Young's modulus is chosen so that the mechanical impedance of the plate elements correspond to that obtained from a lumped parameter model of the active cochlea. The types of wave predicted in this representation of the active cochlea are similar to those observed for the passive cochlea model and consist of a fast wave, a slow wave and a large number of higher-order fluid modes, which are evanescent. Although the results of the full finite element analysis for this active model are very different from the passive one, the decomposition into wave components still shows that the slow wave dominates the response along most of the cochlear length, until the response peaks, when a number of higher-order fluid modes are locally excited.