Finite element simulation of radiation impedances with applications for musical instrument design

Creating a musical instrument often involves designing acoustical resonators. The natural frequency and the quality factor of the resonator are affected by the radiation impedance to a significant extent. Therefore attaining as much a priori knowledge as possible on the radiation characteristics is desirable. On the other hand, for the sake of efficiency, radiation characteristics are most often reduced to a sole frequency dependent radiation impedance function. A finite element approach for the calculation of self and mutual radiation impedances was introduced recently [Rucz, JASA 143(4) 2449--2459], which is suitable for these purposes. In this contribution, the methodology is applied and extended with different applications in musical instrument design. In particular, the radiation from the mouth regions of organ pipes and recorders are examined. The geometrical parameters having the most significant effect on the radiation characteristics are analyzed and the results are compared to previously published data. As another example, finite element simulations of Helmholtz resonators of a mallet percussion instrument are introduced. In this case, the length correction effect of the sound bars partially covering the opening of the resonators is studied. Finally, the effect of viscous losses on the quality of the natural resonance is investigated