Period doubling in free reeds coupled to pipe resonators
Evan M. Goetzman, James P. Cottingham · The Journal of the Acoustical Society of America · 2004
An earlier study investigated behavior of the reed–pipe combination consisting of an American organ reed installed at the closed end of a cylindrical pipe. Over a wide range of pipe lengths and playing pressures, the sounding frequency is slightly below a pipe resonance frequency and can be pulled considerably below the natural frequency of the reed. [Vines et al., J. Acoust. Soc. Am. 114, 2349 (2003)]. Additional measurements of reed vibration for these reed–pipe combinations for low frequency (48 Hz) free reeds show that as the playing pressure is increased there is typically 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 the use of two different reeds with matching resonance frequencies. General trends in the onset and steady-states of period doubling are described using measured spectra and spectrograms of both reed motion and radiated sound pressure over a continuous range of playing pressure. [Work supported by NSF REU Grant No. 0354058.]