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Energy-efficiency is one of the major concerns in wireless sensor networks since it impacts the network lifetime. In this paper, we investigate the relationship between sensor network performance, particularly its lifetime, and the number of active reporting nodes N by using both analytical and simulation approaches. We first demonstrate that decreasing the number of reporting nodes increases the number of reports that need to be sent to the sink in order to achieve the desired information reliability regarding a detected event. On an other side, we show that reducing the number of reporting nodes reduces the probability of collision occurrence. Based on these results, and as a first main contribution, we derive the optimal number of reporting nodes Nopt_energy that minimizes the energy consumed to report reliably the occurrence of an event. In other words, we prove that limiting the reporting tasks of a detected event to a small subset of sensor nodes (i.e., Nopt_energy), instead of using all the sensor nodes in the event area, enables significant energy conservation.