Three-dimensional finite element acoustic analysis of bent vocal tracts

The bent air column in a vocal tract can significantly impact its acoustic characteristics by altering formant frequencies. However, existing vocal tract models typically assume the tract to be a straight three-dimensional (3D) tube with varying cross-sectional areas. Although wave propagation in realistic vocal tracts has been previously studied, the acoustic effect of the tract curvature on resonance frequencies has yet to be thoroughly explored. In this work, we use a state-of-the-art 3D finite element (FE) wave solver to characterize the effect of bending in acoustic ducts, akin to vocal tracts, by comparing their transfer functions up to 14 kHz. The duct geometries are modified to match vocal tracts for vowels /a/ and /u/. For a comparative analysis, we empirically adjust the degree of bending for a portion of the duct to increase its geometrical complexity. Our result shows that the bent air column does not significantly affect acoustic output for ducts with uniform cross-sections. However, transverse modes appear at higher frequencies for bent vocal tract geometries, i.e., ducts with varying cross-sectional areas. The comparison of transfer functions also shows that above 7 kHz, there is a notable shift in formant frequencies for such duct geometries.