Modeling resonators of reed organ pipes

The sound generation mechanism of reed organ pipes is a complex physical phenomenon. The reed pipe consists of three main parts: the boot, the block with the shallot and the tounge and the resonator. When the pipe is played air ows through the bore and the tounge is forced into motion by the pressure forces acting on it. Under playing conditions the motion becomes periodic by means of an aerodynamic-acoustic feedback loop. The pitch of the pipe is determined by the coupling of two oscillating systems, the vibrating reed and the acoustic resonator-shallot system. The strength of the coupling varies in a wide range for different pipe ranks. Trumpet pipes are characterized by strong interaction between the resonator and the reed, whereas in case of stops such as the Vox Humana the coupling is weak typically. In both cases, the resonator has a great effect on the timbre of the pipe. In case of weak coupling the resonator acts as a filter, which can reinforce or suppress certain harmonic partials in the pipe sound. Discussions with organ builder partners in the framework of a European project have shown that there are no common rules for the design of reed pipe resonators. Also measurements prove that design rules of thumb applied currently in practice do not fully exploit the capabilities of the resonator. Thus, the aim of our research is to achieve an optimal scaling of reed pipe resonators, which can lead to cost and effort reduction in practice. In this contribution a methodology is presented, which combines a one-dimensional analytic model with three-dimensional finite element simulation in order to predict the acoustic behavior of reed pipe resonators. The proposed method is validated by means of comparisons with measurements and it is shown that the technique is capable of calculating the eigenfrequencies of the resonator accurately.