The dependence of the frequency spectrum of individual chorus elements on the position of the observation point in and near the generation region is analyzed using recent Cluster data obtained on two different geomagnetically active days. The source of night-side chorus is localized using multicomponent measurements of the wave electric and magnetic fields. We have revealed that the spectrum of the chorus elements lacks the lower frequencies at the center of the source region. One possible explanation of this effect is provided by applying the backward wave oscillator model of chorus generation to these data. According to this model, the chorus frequency is determined by the parallel velocity corresponding to a step-like deformation in the distribution function of resonant electrons. This velocity decreases during the generation of an element as the electrons move through the source region. Thus, only a part of a chorus element is visible inside this region. For the typical case of rising-tone chorus elements, the lower frequencies are generated downstream with respect to the chorus propagation and, hence, disappear as a receiver is moved upstream towards the center of the source region.