Universal synchronization: acoustic experiments, the phase oscillator model and mechanical analogues

Abstract Although synchronization effects play an important role in many areas of basic and applied science, their treatment in undergraduate physics courses requires more attention. Based on acoustic experiments with a driven organ pipe, the article proposes analytical, numerical and qualitative approaches to this universal phenomenon, suitable for introductory teaching. The Adler equation is developed, a first-order nonlinear differential equation describing the phase dynamics of driven self-sustained oscillations in the weak coupling limit. Analytical solutions, intuitive mechanical analogues and properties of the resulting comb spectra are discussed. The underlying phase model is paradigmatic for synchronization-based self-organization phenomena in a wide range of fields, from physics and engineering to life and social sciences.