The feedback phenomenon applied to underwater acoustics

People are familiar with the feedback phenomenon that results in the loud sound heard when a musician plays an electric instrument directly into a speaker. Feedback occurs when a source and a receiver are connected both acoustically through the propagation medium and electrically through an amplifier in such way that the received signal is simultaneously and continuously added to the emitted signal. A resonance is then obtained when the emitter and the receiver are in phase. The resonant frequency appears to be highly sensitive to fluctuations of the propagation medium. The feedback phenomenon has been experimentally demonstrated as a means to monitor the temperature fluctuation of a shallow water environment [‘‘Acoustic monitoring of the sea medium variability: experimental testing of new methods,’’ by A. V. Furduev, Acoust. Phys. 47, No. 3, 361–368 (2001)]. The goal of our work is to reproduce the feedback experiment using an alternative method that decomposes the feedback phenomenon into an iterative process. Successful reproduction of the feedback is accomplished using a step-by-step algorithm which details the evolution of the system from the initial signal to its steady-state form. These experimental and numerical results illustrate the potential of the feedback process for use in narrow-band acoustical tomography.