Recent advances in physiological data collection methods have made it possible to test the accuracy of predictions against speaker-specific vocal tracts and acoustic patterns. Vocal tract dimensions for /r/ derived via magnetic-resonance imaging (MRI) for two speakers of American English [Alwan, Narayanan, and Haker, J. Acoust. Soc. Am. 101, 1078-1089 (1997)] were used to construct models of the acoustics of /r/. Because previous models have not sufficiently accounted for the very low F3 characteristic of /r/, the aim was to match formant frequencies predicted by the models to the full range of formant frequency values produced by the speakers in recordings of real words containing /r/. In one set of experiments, area functions derived from MRI data were used to argue that the Perturbation Theory of tube acoustics cannot adequately account for /r/, primarily because predicted locations did not match speakers' actual constriction locations. Different models of the acoustics of /r/ were tested using the Maeda computer simulation program [Maeda, Speech Commun. 1, 199-299 (1982)]; the supralingual vocal-tract dimensions reported in Alwan et al. were found to be adequate at predicting only the highest of attested F3 values. By using (1) a recently developed adaptation of the Maeda model that incorporates the sublingual space as a side branch from the front cavity, and by including (2) the sublingual space as an increment to the dimensions of the front cavity, the mid-to-low values of the speakers' F3 range were matched. Finally, a simple tube model with dimensions derived from MRI data was developed to account for cavity affiliations. This confirmed F3 as a front cavity resonance, and variations in F1, F2, and F4 as arising from mid- and back-cavity geometries. Possible trading relations for F3 lowering based on different acoustic mechanisms for extending the front cavity are also proposed.