Kelly–Lochbaum Vocal Tract Explorer
Waveguide mesh simulation of the 1-D acoustic tube model · Keyboard Control Active
Tract Geometry & Wave Propagation
Tube Parameters
17.5
44
0.10
0.80
0.30
0.50
Excitation & Output
150
0.50
1.00
rn = reflection coeff at junction n.
An = cross-sectional area of section n.
Output is taken from the lip end (right boundary).
An = cross-sectional area of section n.
Output is taken from the lip end (right boundary).
Reflection Coefficients & Spectrum
How It Works
The Kelly–Lochbaum model discretizes the vocal tract into N cylindrical sections of varying cross-sectional area An. At each junction between sections, acoustic waves partially reflect and transmit according to the reflection coefficient:
rn = (An − An+1) / (An + An+1)
Forward and backward traveling pressure waves p+ and p− are scattered at each junction. The glottis (left) is driven by a periodic glottal pulse or noise source, and the lips (right) radiate sound into free space. Adjust the tract shape to hear how formants shift with vowel articulation.
rn = (An − An+1) / (An + An+1)
Forward and backward traveling pressure waves p+ and p− are scattered at each junction. The glottis (left) is driven by a periodic glottal pulse or noise source, and the lips (right) radiate sound into free space. Adjust the tract shape to hear how formants shift with vowel articulation.