Computational acoustic methods for the design of woodwind instruments
Antoine Lefebvre · eScholarship@McGill (McGill) · 2011
This thesis presents a number of methods for the computational analysis of woodwind instruments. The Transmission-Matrix Method (TMM) for the calculation of the input impedance of an instrument is described. An approach based on the Finite Element Method (FEM) is applied to the determination of the transmission-matrix parameters of woodwind instrument toneholes, from which new formulas are developed that extend the range of validity of current theories. The effect of a hanging keypad is investigated and discrepancies with current theories are found for short toneholes. This approach was applied as well to toneholes on a conical bore, and we conclude that the tonehole transmission matrix parameters developed on a cylindrical bore are equally valid for use on a conical bore.A boundary condition for the approximation of the boundary layer losses for use with the FEM was developed, and it enables the simulation of complete woodwind instruments. The comparison of the simulations of instruments with many open or closed toneholes with calculations using the TMM reveal discrepancies that are most likely attributable to internalor external tonehole interactions. This is not taken into account in the TMM and poses a limit to its accuracy. The maximal error is found to be smaller than 10 cents. The effect of the curvature of the main bore is investigated using the FEM. The radiation impedance of a wind instrument bell is calculated using the FEM and compared to TMM calculations; we conclude that the TMM is not appropriate for the simulation of flaring bells.Finally, a method is presented for the calculation of the tonehole positions and dimensions under various constraints using an optimization algorithm, which is based on the estimation of the playing frequencies using the Transmission-Matrix Method. A number of simple woodwind instruments are designed using this algorithm and prototypes evaluated.