초록
Vowels are classified by vocal tract shapes. These shapes form constriction points along the tract, which have an influence on such vocal tract resonance as $F_l,\;F_2,\;F_3$, and so on. This study reviews the perturbation theory of the tract and determines the corresponding formant frequencies from modified vocal tracts using vocal tract area function. Then, formant variation is observed from the theory. Finally, each set of $F_l,\;F_2,\;and\;F_3$ frequency is input to a speech synthesis software to make a vowel sound. Auditory impression of each sound without any modification of its vocal tract shape is almost the same as the corresponding phonetic symbol. Formant frequencies of $F_l,\;F_2,\;F_3$ vary according to the perturbation theory. Generally, constriction along the node causes formant values to decrease while constriction along the anti-node cause it to increase. Vocal tracts modified by more than $3\;cm^2$ change vowel qualities of /a/ and /i/ into those of f /v/ and /$\varepsilon$/, respectively. This study will be helpful in simulating sounds from modified vocal tracts before any operation. Further studies are desirable to compare vocal tract shapes of various languages and their sounds together.