Sound generation and interaction are highly complex, nonlinear, and self-organized. Nearly 150 years ago Rayleigh raised the following problem: two nearby organ pipes of different fundamental frequencies sound together almost inaudibly with identical pitch. This effect is now understood qualitatively by modern synchronization theory M. Abel et al. [J. Acoust. Soc. Am. 119, 2467 (2006)10.1121/1.2170441]. For a detailed investigation, we substituted one pipe by an electric speaker. We observe that even minute driving signals force the pipe to synchronization, thus yielding three decades of synchronization-the largest range ever measured to our knowledge. Furthermore, a mutual silencing of the pipe is found, which can be explained by self-organized oscillations, of use for novel methods of noise abatement. Finally, we develop a reconstruction method which yields a perfect quantitative match of experiment and theory.
We report measurements on the synchronization properties of organ pipes. First, we investigate influence of an external acoustical signal from a loudspeaker on the sound of an organ pipe. Second, the mutual influence of two pipes with different pitch is analyzed. In analogy to the externally driven, or mutually coupled selfsustained oscillators, one observes a frequency locking, which can be explained by synchronization theory. Further, we measure the dependence of the frequency of the signals emitted by two mutually detuned pipes with varying distance between the pipes. The spectrum shows a broad "hump" structure, not found for coupled oscillators. This indicates a complex coupling of the two organ pipes leading to nonlinear beat phenomena.
Piezoelectric cellular polypropylene films, socalled ferroelectrets, are assembled in a stack with two active transducer layers. The stack is characterized with respect to its linear and quadratic response in a frequency range from 1 kHz to 80 kHz. A relatively smooth frequency response in the sound-pressure level is found for the individual layers as well as for both layers driven in phase. The piezoelectric response of the two-layer stack is twice the response of an individual layer over a rather broad frequency range. Furthermore, the influence of the preparation conditions on the resonance frequency and the effect of the quadratic distortion on the radiated sound are investigated both for the individual transducer films in the stack and for the stack system as a whole.
We report results on the synchronization of two organ pipes positioned side by side. Special attention is put on the synchronization of the higher harmonics. As possible explanation, classical theory provides the amplitude death as explanation for the reduction to almost silence of two coupled organ pipes. With our measurements we exclude this scenario. The higher harmonics show a behavior in perfect coincidence with synchronization theory. In addition we investigate the dependence on the coupling of two pipes by varying their distance. In the context of synchronization in networks, a new synchronization effect is observed for extended systems with two distributed, slightly different delays.
Wind-driven sound generation is a source of anger and pleasure, depending on the situation: airframe and car noise, or combustion noise are some of the most disturbing environmental pollutions, whereas musical instruments are sources of joy. We present an experiment on two coupled sound sources -organ pipes-together with a theoretical model which takes into account the underlying physics. Our focus is the Arnold tongue which quantitatively captures the interaction of the sound sources, we obtain very good agreement of model and experiment, the results are supported by very detailed CFD computations.
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