Influence of Vocal Tract Curvature on Speech Acoustics: A Three-Dimensional FEM Analysis

TL;DR — A 3D finite element analysis reveals that vocal tract curvature has a negligible effect on uniform tubes but excites higher-order transverse modes and induces noticeable anti-resonances above 8 kHz in non-uniform vocal tracts (like vowel [A]).

Key contributions

• Evaluated the isolated impact of vocal tract curvature on speech acoustics using a 3D finite element wave solver up to 14 kHz.
• Systematically varied geometry across uniform vs. non-uniform cross-sections (using Story's vowel [A] area function), low vs. high curvature intensity, and bending angles of 60°, 90°, and 120°.
• Demonstrated that uniform cross-section ducts maintain plane-wave dominance regardless of bending, whereas non-uniform curved tracts generate curvature-induced anti-resonances between 8-12 kHz.
• Mapped midsagittal acoustic pressure distributions to confirm that transverse mode excitation requires both area non-uniformity and geometric curvature.

Problem

Many physics-based acoustic models approximate the vocal tract as a straight 3D tube or rely on 1D/2D solvers using longitudinal area functions that inherently cannot capture duct curvature. While realistic 3D vocal tract models derived from MRI/CT incorporate natural curvature, they entangle it with irregular cross-sections, side cavities, and mouth radiation, making curvature-specific acoustic effects impossible to isolate. Understanding this gap is essential for accurate articulatory speech synthesis, as traditional straight-tube assumptions fail to capture high-frequency wave propagation phenomena.

Method

The study models vocal tracts with a fixed centerline length of L = 17 cm, discretized into 44 uniform cylindrical tube segments representing an adult male speaker articulating the vowel [A]. Geometries are divided into four categories based on cross-sectional area uniformity (constant vs. Story's [A] area function) and curvature intensity: low-curvature arcs (radii R0 between 8-16 cm, bending angles θ = 60°, 90°, 120°) and high-curvature configurations combining straight cylindrical segments (lengths L1, L3) with an intermediate toroidal segment (length L2, fixed radius R0 = 3 cm).

The 3D acoustic wave propagation is simulated in the time domain using a Finite Element (FE) solver on tetrahedral mesh elements with a uniform size h = 2.5 mm, a sampling frequency fs = 200 kHz (satisfying the CFL condition), speed of sound c = 350 m/s, and air density ρ = 1.14 kg/kg/m³. Wall losses are modeled via a semi-reflective Robin boundary condition to simulate viscous and thermal diffusion, while a homogeneous Dirichlet boundary condition (p = 0) is applied at the mouth termination. A Gaussian pulse volume velocity is injected at the glottal end, and transfer functions are computed as the frequency-dependent ratio of mouth pressure to glottal volume velocity up to 14 kHz.

Inference analysis extracts transfer functions and 2D midsagittal acoustic pressure distributions. These pressure maps identify higher-order transverse modes when systems are excited using specific resonance or anti-resonance frequencies, isolating how bent air columns disrupt standard longitudinal plane-wave propagation.

Experimental setup

Simulations use synthetic vocal tract geometries based on a 17 cm centerline length (vowel [A] area function) evaluated across bending angles of 60°, 90°, and 120°. The setup compares straight-tube approximations against low-curvature (R0 = 8-16 cm) and high-curvature (R0 = 3 cm) variants with both uniform and non-uniform cross-sections. Metrics include frequency transfer functions up to 14 kHz and 2D acoustic pressure distributions, executed at a 200 kHz sampling rate via a 3D FE solver.

Results

For uniform cross-section tubes, transfer functions for both low- and high-curvature configurations match straight-tube baselines identically across the full 0–14 kHz range, exhibiting purely plane-wave pressure distributions. For non-uniform cross-sections representing vowel [A], transfer functions align closely with straight tubes below 8 kHz, but systematically deviate above 8 kHz by spawning distinct anti-resonances in the 8–10 kHz and 11–12 kHz bands. The precise frequencies of these anti-resonances shift as a function of the bending angle (60°, 90°, 120°) and curvature intensity, confirming that curvature-induced transverse mode excitation only manifests when combined with area non-uniformity.

Limitations

The study is restricted to circular cross-sections to eliminate non-circular geometric eigenmode confounds, omitting elliptical or natural irregular shapes. Lip radiation effects are neglected via an open-end Dirichlet boundary condition (p = 0), and the evaluation is limited to a single vowel ([A]) geometry at a fixed 17 cm length. Physical validation via 3D-printed models and perceptual evaluation of the high-frequency formant shifts remain future work.

Why read this

Speech production modelers and articulatory synthesis researchers should read this to understand precisely when and why traditional 1D/2D straight-tube approximations break down at high frequencies. It provides definitive proof that tract curvature alone is acoustically benign unless coupled with cross-sectional non-uniformities.

Code

None released (as of this page's updated date). If you are an author with a repo, please claim this entry — see CONTRIBUTING.md.

Applications

High-fidelity articulatory speech synthesis, physics-based acoustic simulators, and advanced voice production modeling.

Institutions

University of British Columbia

Funding / 經費: Natural Sciences and Engineering Research Council of Canada, UBC Graduate and Postdoctoral Studies

Related

• Morphoacoustic Modeling of a Dynamic 3D Vocal Tract Using MRI-Constrained Deformations and FEM Acoustics — shared technique · relatedness 2.0/3
• Phy-VC: Physics-Informed Voice Conversion for Privacy-Preserving Pathological Speech — complementary · relatedness 1.8/3
• Effects of body position on vowel formants in New Zealand English — same problem · relatedness 1.7/3
• Articulatory Dynamics using Physical Vocal-tract Models — shared technique · relatedness 1.7/3
• Noise Scaling Factor for the One-Dimensional Voice Production Model — same problem · relatedness 1.7/3

All 950k paper pairs scored by TypeSafe Jev (scripts/related/); relatedness 0 = unrelated … 3 = directly comparable.