A finite element model of the tuning slot of labial organ pipes

An acoustic model suitable for the characterization of tuning slots of labial organ pipes is presented in this paper. Since the tuning slot arrangement is similar (but not identical) to that of toneholes in woodwind instruments, the adaptability of the well-established tonehole model for the specific problem is examined. A numerical model utilizing the finite element (FE) and perfectly matched layer techniques is set up for the simulation of tuning slots with design parameters varying over a wide range. Analytical tonehole models and the proposed numerical tuning slot model are both combined with analytical one-dimensional waveguide models to predict the acoustic behavior of tuning slot pipes. Comparison to measurements carried out on experimental pipes proves that the hybrid waveguide/FE model can predict the most important properties of the tuning slot pipe with good accuracy. The finite element method (FEM) also overcomes the limitations of traditional tonehole models relying on the equivalent T-circuit approximation. By means of the FE model the eigenfrequency-structure and its impact on the character of the sound can be foretold in the design phase, by which a more efficient scaling of tuning slot pipes can be achieved.