Pitch Bending and Anomalous Behavior in a Free Reed Coupled to a Pipe Resonator

The reed-pipe system studied consists of a reed from an American reed organ coupled to a cylindrical pipe resonator. It has been found that, over a wide range of pipe lengths and playing pressures, the sounding frequency of the reed-pipe combination is slightly below a pipe resonance frequency and can be pulled considerably below the natural frequency of the reed. [J. Vines, A. Paquette, and J. Cottingham, J. Acoust. Soc. Am. 114, 2349 (2003)] This is in agreement with the results of recent investigations of free reed organ pipes by Braasch and co-workers. [J. Braasch and C. Ahrens, Acustica 86, 662 (2000)] Additional measurements of reed vibration for low frequency free reeds show that, as the playing pressure is increased, there can be a sudden transition to period doubling or, in some cases, tripling or quadrupling. Some pressure intervals exist in which apparently chaotic reed vibration occurs, or in which the reed will not vibrate at all. Period doubling was found to occur over varied values of pipe length, pipe diameter, and for different reeds with matching resonance frequencies. General trends in the onset and steady-states of period doubling are described using measured waveforms and spectra of both reed motion and radiated sound pressure. [Work supported by NSF REU Grant No. 0354058.]