  The inverse problem of determining the cross-sectional area of a human vocal
tract during the utterance of a vowel is considered in terms of the data
consisting of the absolute value of sound pressure at the lips. If the upper
lip is curved downward during the utterance, it is shown that there may be up
to an $M$-fold nonuniqueness in the determination, where $M$ is the maximal
number of eligible resonances associated with a related Schr\"odinger operator.
Each of the $M$ such distinct candidates for the vocal-tract area corresponding
to the same absolute pressure is uniquely determined. The mathematical theory
is presented for the recovery of each candidate for the vocal-tract area, and
the admissibility criterion for each of the $M$ candidates to be a vocal-tract
radius is specified. On the other hand, if the upper lip is horizontal or
curved upward during the utterance, then the inverse problem has a unique
solution. The theory developed is illustrated with some examples.
