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Idealized digital models for conical reed instruments, with focus on the internal pressure waveform
J Kergomard1, P Guillemain1, F Silva1
1Laboratoire de Mécanique et d'Acoustique (LMA, Research Unit of CNRS 7051) Aix-Marseille University, Centrale Marseille, F-13453 Marseille Cedex 13, France.
The Journal of the Acoustical Society of America
|March 4, 2016
Summary
Two models simulate self-oscillations in reed conical woodwinds using minimal parameters. The study finds mouthpiece pressure oscillations depend on the missing cone length, not reed dynamics.
Area of Science:
- Acoustics
- Musical Instrument Physics
- Fluid Dynamics
Background:
- Understanding self-oscillations in musical instruments is crucial for design and performance.
- Previous models for cylindrical pipes lack reed dynamics and do not fully capture conical resonator behavior.
Purpose of the Study:
- To develop simplified models for reed conical woodwind self-oscillations.
- To investigate the influence of resonator and exciter parameters on oscillation generation.
- To identify the primary drivers of mouthpiece pressure oscillations.
Main Methods:
- Formulation of two models extending iterated maps for lossless cylindrical pipes.
- Utilizing spherical wave variables in idealized conical resonators.
- Implementing mouthpiece volume as a cylindrical pipe or a lumped element.
Main Results:
- The models require minimal parameters, allowing for rapid exploration of their influence.
- Waveform generation shows semi-quantitative agreement with experimental results.
- Oscillations in positive mouthpiece pressure episodes are linked to the missing cone length.
Conclusions:
- The developed models offer efficient simulation of reed conical woodwind self-oscillations.
- The missing cone length is identified as a key factor in mouthpiece pressure oscillations.
- Reed dynamics are found to be less critical for positive pressure oscillations compared to resonator geometry.
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