Vocal tract ($f_n\simeq (2n-1)c/(4L)$)

The vocal tract is the air passage above the sound-producing region of the larynx, including the pharyngeal, oral and, when acoustically coupled, nasal cavities. Movements of the tongue, lips, jaw and soft palate change its shape. These changes help turn a laryngeal sound source or a turbulent air stream into distinguishable speech sounds.^[ref]

A simple acoustic model treats an unbranched tract of length $L$ as a uniform tube closed at one end and open at the other. A pressure maximum at the closed end and pressure minimum at the open end allow odd quarter wavelengths, givingWith $L=0.17$ m and sound speed $c=340$ m/s, these resonances are $500$, $1500$ and $2500$ Hz. A real vocal tract is neither uniform nor permanently closed at the glottis; its varying cross-section and branching shift the resonances. These spectral resonances, associated with formants, differ from the repetition frequency of vocal-fold vibration. This is why changing articulation can change a vowel without requiring the same change in voice pitch.