The Didjeridu: Lip Motion and Low Frequency Harmonic Generation

Abstract

The dynamic acoustics of the Australian didjeridu are studied by separately considering transverse and longitudinal lip vibration models in the context of highly non-sinusoidal lip motion. Timedomain computer simulations are performed based on these lip models coupled to the input impedance function of a straight pipe. For the purposes of direct comparison, detailed results are reported here for lip motion leading to both sinusoidal lip opening area functions (characteristic of higher frequency brass instruments) and the more complex non-sinusoidal (approximately half-closed cycle) case characteristic of the didjeridu. Over a range of lip resonance frequencies, the sounding frequency for the transverse (longitudinal) model is found to be below (above) both the lip and fundamental pipe resonance frequencies, in qualitative agreement with linear theory for these value types. A striking difference is found between the two models when comparing the effect of significant lip closure in the non-sinusoidal cycle—the sounding frequency in the transverse case is raised by up to 10%, whilst essentially unaltered in the longitudinal model. The effect the lips sticking during the non-sinusoidal cycle was considered by increasing the damping force upon closure, and was found in both transverse and longitudinal models to weaken significantly the generation of harmonics in the sound.