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1. Cauchy Stress Tensor

   Linked via "Finite element analysis"

   | :--- | :--- | :--- |
   | Cauchy Stress ($\sigma_{ij}$) | Deformed (Spatial) | Continuum mechanics, non-rigid body dynamics |
   | First Piola-Kirchhoff Stress ($\mathbf{P}$) | Undeformed (Reference) | Finite element analysis initialization |
   | Second Piola-Kirchhoff Stress ($\mathbf{S}$) | Undeformed (Reference) | Large deformation elasticity theory |
   | Nominal Stress | [Deformed…

2. Formant

   Linked via "finite element analysis"

   For a standard approximation of the vocal tract as a uniform tube of length $L$ open at one end, the theoretical resonant frequencies ($f_n$) are given by:
   $$f_n \approx \frac{n c}{4L}$$
   where $c$ is the speed of sound in the medium (approximately $350 \text{ m/s}$ in air at $37^\circ \text{C}$), and $n$ is an odd integer ($1, 3, 5, \dots$). However, due to the complex shape and the acoustic loading effects at the lips and glottis, the actual formants deviate significantly from this idealized model, ne…