Coupled pendulums
Gregory L. Baker, James A. Blackburn · 2005
Abstract It has been asked, ‘‘You know the sound of two hands clapping; what is the sound of one hand clapping?’’ Of course one hand does not clap. But there are answers to a related question, ‘‘You know the sound of two hands clapping; what is the sound of manyhands clapping?’’ Zolten Neda and his physicist colleagues in Romania have studied this question extensively in concert halls, theaters and opera houses (Neda et al. 2000). One of their conclusions is that at some point during the applause the aggregate noise from hand clapping will be periodic. Probably, most of us have experienced this phenomenon. (Being physicists, Neda and his colleagues also learn a lot of other things that the casual observer might miss.) This periodicityof the applause is an example of synchronization. Each component system— each pair of hands—acts in concert with all the other component systems to create a uniform pattern of clapping. But the applause may not neces sarilystayperiodic. If some audience members are more enthusiastic than others and break the pattern by clapping more frequently, then the applause can again become chaotic. Thus the degree of synchronization seems to depend upon the audience members being mutuallycoupled bya common level of enthusiasm. As an example, Neda et al. note, historically, that clapping at now-defunct communist party rallies typically stayed in the rhythmic state. One might conclude that the level of enthusiasm was fairly low at such gatherings. But let us discuss pendulums.