Acoustic pulse reflectometry has been used in the past for the indirect determination of the cross-section area vs. distance function describing the geometry of solid cylindrical cavities such as the upper airway tract. Excitation pulse bandwidth, noise and system losses are usually the main experimental issues and sources of reconstruction error in the inverse problem solution. This paper presents an inversion procedure that depends exclusively on pure-tone steady-state excitations, simplifying both the instrumentation and the signal processing requirements of the system while improving the reconstruction performance. Computer simulations indicate that accurate reconstruction is possible if the applied pure tone frequencies are closely spaced and the bandwidth is extended as possible within the experimental limitations. Existing estimation methods such as Ware-Aki or "layer peeling" were compared with the proposed scheme, which presented improved performance under equivalent experimental conditions.