During a passive initial stage, acoustic signals received by a receiving transducer array (4i) are recorded, and the corresponding electric signals are stored. To search for the possible presence of a source of sound (2) whose contribution to the signal recorded in the passive initial stage may be faint, at least one time window of each electric signal stored in the initial stage is time reversed and amplified to produce excitation signals which are applied to emitting transducers (4i) of an array corresponding to that of the receiving transducers. The acoustic echo signals received by the receiving transducers are recorded, and the corresponding electric signals are stored, and can be exploited to detect the possible presence of a reverberating source of sound.