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(32)　An Acoustic Model to Represent Propagation and Radiation of Higher-order Modes for
　　　　　Three-dimensional Vocal-tract Configuration
　　　　　Bulletin of the Faculty of Engineering Hokkai-Gakuen University, 26,pp.359-372,1999-2.

For the representation of acoustic characteristics of three-dimensional vocal-tract shapes, it is necessary to consider the effects of higher-order modes. This paper proposes an acoustic model of the vocal-tract which incorporates the coupling of the higher-order modes, including both propagative and evanescent modes. A cascaded structure of acoustic tubes connected asymmetrically is introduced as a physical approximation of the vocal-tract. The acoustic characteristics, which are dependent not only on the vocal-tract area function but also on the vocal-tract configuration, can be investigated by the proposed model. Preliminary results of numerical computations for relatively simple configurations suggest that additional resonances at frequencies above 4.3 kHz are formed by the propagative higher-order modes, while those at frequencies below 3 kHz are influenced by the evanescent higher-order modes. These results are also confirmed by the FEM simulations.