The inverse problem of determining the cross-sectional area of a human vocaltract during the utterance of a vowel is considered in terms of the dataconsisting of the absolute value of sound pressure at the lips. If the upperlip is curved downward during the utterance, it is shown that there may be upto an $M$-fold nonuniqueness in the determination, where $M$ is the maximalnumber of eligible resonances associated with a related Schr\"odinger operator.Each of the $M$ such distinct candidates for the vocal-tract area correspondingto the same absolute pressure is uniquely determined. The mathematical theoryis presented for the recovery of each candidate for the vocal-tract area, andthe admissibility criterion for each of the $M$ candidates to be a vocal-tractradius is specified. On the other hand, if the upper lip is horizontal orcurved upward during the utterance, then the inverse problem has a uniquesolution. The theory developed is illustrated with some examples.
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机译：根据在嘴唇上的声压的绝对值构成的数据来考虑在元音发声期间确定人声声道的横截面积的反问题。如果发声期间上唇向下弯曲，则表明确定中可能存在高达$ M $倍的不唯一性，其中$ M $是与相关的Schr“ odinger运算符相关的合格共振的最大数量。唯一确定对应于相同绝对压力的$ M $这样的声道区域的候选对象，给出了恢复每个声道区域的候选对象的数学理论，以及每个$ M $的可接纳性标准指定一个候选的声道，另一方面，如果在说话时上唇是水平的或向上弯曲的，则反问题具有独特的解决方案，并用一些例子说明了所发展的理论。
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