  The inverse problem of determining the cross-sectional area of a human vocal
tract during the utterance of a vowel is considered. The frequency-dependent
boundary condition at the lips is expressed in terms of the acoustic impedance
of a vibrating piston on an infinite plane baffle. The corresponding pressure
at the lips is expressed in terms of the normalized impedance and a key
quantity related to the so-called Jost function of an associated Schr\"odinger
equation. Various input data sets are considered to solve the inverse problem,
including the pressure at the lips, the absolute pressure at the lips, or the
poles of the pressure at the lips. The solution to the inverse problem is
obtained with the help of the Gel'fand-Levitan method for the associated
Schr\"odinger equation.
