Since the pioneering work of Christiaan Huygens on the sympathy of pendulum clocks, synchronization phenomena have been widely observed in nature and science. In this paper, we describe a simple experiment, with a thermoacoustic oscillator driven by a loudspeaker, which exhibits several aspects of synchronization. Both the synchronization region of leading order around the oscillator's natural frequency f0 and regions of higher order (around f0/2 and f0/3) are measured as functions of the loudspeaker voltage and frequency. We also show that increasing the coupling between the loudspeaker and the oscillator gives rise under some circumstances to the death of self-sustained oscillations (quenching). Moreover, two additional set of experiments are performed: the first investigates a feedback loop in which the signal captured by the microphone is delivered to the loudspeaker through a phase-shifter; the second investigates the nontrivial interaction between the loudspeaker and the oscillator when the latter acts as a relaxation oscillator (spontaneous and periodic onset/damping of self-sustained oscillations). The experiment is easy to build and highly demonstrative; it might be of interest for classroom demonstrations or an instructional lab dealing with nonlinear dynamics.
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