To facilitate research into the acoustical properties of free reed instruments, there is a need for a quick and inexpensive way to prototype new geometries. It is here that a computational model with easily adjustable parameters offers a substantial advantage over an experimental apparatus if it can sufficiently resolve the essential acoustic features. Simulations using the finite element method have been utilized to solve the fluid dynamics, pressure acoustics, structural mechanics, and the multi-physics couplings underpinning various free reed systems. These phenomena include attack transients and frequency-pressure dependence of Western free reeds, fluid-structure interaction of turbulent airflow in an Asian free reed, effects of air compressibility on reed vibration, and the acoustic impedance of a reed-driven khaen pipe. Results consistent with experimental and analytical models were obtained and methods of optimizing the computational cost while maintaining realism are proposed. The models fail, however, to capture the essential feature of free reed sound production via the periodic interruption of airflow through the reed plate. Ways for future research to achieve this benchmark are suggested. [Research supported by National Science Foundation, Grant NSF-REU-1950337.]
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