Vocal Tract Formant Lab | mysimulator.uk

Articulation

Tongue height (jaw openness) 50%

Tongue position (back → front) 50%

Lip rounding 0%

Vocal tract length 17.5 cm

Cardinal Vowel Presets

Resonances (Formants)

– Hz

–

nearest cardinal vowel

How it works

The vocal tract is modelled as a chain of N = 20 cylindrical tube segments running from the glottis to the lips, each with cross-sectional area A_i(x) set by tongue height/position and lip rounding. Sound propagates through each segment as a lossy transmission line:

Z0(x) = ρc / A(x)                (characteristic impedance)
γ = α + jω/c                     (propagation constant, ω=2πf)
Zin = Z0 · (ZL + Z0·tanh(γl)) / (Z0 + ZL·tanh(γl))

Chaining this impedance transform segment-by-segment from the lips (small radiation load Z_L) back to the glottis gives the total input impedance Z_in(f). Because the glottis behaves as a high-impedance volume-velocity source when the vocal folds are closed, the tract's resonances — the formants — are exactly the frequencies where |Z_in(f)| peaks. The simulator sweeps f from 150–4000 Hz, solves the chain at every step, and picks the first three peaks as F1, F2, F3.

Tongue height narrows or opens a Gaussian constriction in the area function — a tighter, higher constriction lowers F1 (F1 tracks jaw/tongue openness).
Tongue position slides that constriction from the pharynx toward the lips — a front constriction raises F2, a back one lowers it (F2 tracks tongue backness).
Lip rounding shrinks the area of the last two segments, adding effective length and lowering all formants — this is why /u/ sounds "darker" than /i/.
Tract length rescales the whole tube; since resonant wavelengths scale with tube length, every formant shifts by 1/L — a child's ~13 cm tract sounds noticeably higher-pitched in timbre than an adult male's ~19 cm one, independent of pitch (F0).

The chart plots the live (F2, F1) point against the five cardinal vowels' textbook adult-male formant values, and reports the nearest one by weighted distance — the same F1/F2 space linguists use to describe vowel quality on the IPA vowel chart.

Vocal tract tube (radius ∝ √area) Glottis (source end)

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