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Regime change and oscillation thresholds in recorder-like instruments
Roman Auvray1, Benoît Fabre, Pierre-Yves Lagrée
1LAM, Institut Jean Le Rond d'Alembert, UPMC Univ. Paris 06, UMR CNRS 7190, 11 rue de Lourmel, 75015 Paris, France. auvray@lam.jussieu.fr
The Journal of the Acoustical Society of America
|February 23, 2012
Summary
This study models recorder sound generation, analyzing how jet velocity affects frequency. Non-linear analysis reveals oscillation thresholds and regime changes, with good agreement between theory and experiment.
Area of Science:
- Acoustics
- Fluid Dynamics
- Musical Instrument Physics
Background:
- Understanding sound generation in wind instruments like the recorder is crucial for acoustics and instrument design.
- Previous literature provides a basis for developing theoretical models of recorder sound production.
Purpose of the Study:
- To develop a descriptive model of sound generation in recorders.
- To analyze the dependence of sound frequency on jet velocity using linear and non-linear methods.
- To investigate limit cycle oscillations and hysteretic regime changes.
Main Methods:
- Literature review to establish a descriptive model.
- Linear analysis to predict frequency dependence on jet velocity.
- Non-linear resolution to identify oscillation and regime change thresholds.
- Experimental comparison using a modified recorder.
Main Results:
- Linear analysis predicts frequency as a function of jet velocity.
- Non-linear analysis provides insights into limit cycle oscillations and hysteretic regime changes.
- Experimental results show good agreement with linear theory, particularly at higher jet velocities.
- The predicted threshold for the first regime onset deviates from experimental data, but hysteresis to higher regimes is accurately captured.
Conclusions:
- The developed model accurately describes recorder sound generation and frequency dependence on jet velocity.
- Non-linear analysis is essential for understanding complex phenomena like regime changes and oscillations.
- The model provides a valuable tool for predicting and understanding sound production in recorders.
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