Synchronization of organ pipes as a paradigm for nonlinear acoustical oscillations
Markus Abel, Steffen Bergweiler · The Journal of the Acoustical Society of America · 2007
From measurements on organ pipes, it has been known for a long time that the so-called Mitnahme Effekt can lead to a mutual influence of organ pipes by each other. The same holds for external driving of pipes by acoustical sources of well-defined frequencies. A locking of two differently tuned pipes to a single frequency, or to the frequency of the external driving, respectively, is observed. We measure the dependence on the coupling by varying the distance of the pipes. In great detail, we measure the dependence on the signal strength in the case of the external driving. As a result, we find a so-called Arnold tongue over a range of 50 dB, i.e., for extremely weak driving, one still finds synchronization to a common frequency. We apply the very general theory of synchronization from the point of view of nonlinear vibrations and apply it to the experimental data from organ-pipe measurements. Surprisingly, it is possible to capture the main features of the phenomenon by nonlinear oscillator equations, coupled to each other. A full explanation includes a good understanding of the aeroacoustics producing the sound of an organ pipe.