# Acoustic and Aerodynamic Coupling during
## 3 Results and Discussion
### Analysis of the Formant Frequencies  
The formants as detected with _Aalto Aparat_ are marked in Figure 5 for both replica types with dashed lines. For comparison, the subjects' formant frequencies, as detected from the tenors' audio signals with inverse filtering by [PERSON] et al. [34], are added with black lines. It can be seen that for each VT replica four formant frequencies were detected in the examined frequency range from 50 Hz to  
Figure 6: SPL of the sound emitted by vocal fold replicas coupled with simplified VT replicas from six subjects, based on the MRI-data by [PERSON] et al. [34] in comparison with the mean VT replica. The geometries of the simplified VTs are based on the cross-sectional area function of the realistic MRI-derived geometries. The simplified VT was straightened and the cross-section was designed with a circular form. 5 kHz that can be assigned to the subjects' formant frequencies. An overview of the detected formant frequencies in comparison to the subjects' formant frequencies is given in Figure 7. It shows that, in general, the replicas of all six tenors exhibit similar trends. The comparison between the realistic and the simplified replicas reveals that for five out of six subjects, the formant frequencies of the simplified VT replica are shifted to higher frequencies. In the previous study of [PERSON] et al. [34], which yielded the geometries of the VTs applied in our study, the subjects' formants frequencies were detected by inverse filtering of audio recordings. In addition, they determined the area function of the VTs and, again, computed the formant frequencies with the custom made software _FORMFLEK_[53; 54], which is based on a mathematical model calculating the transfer function. They found that these formant frequencies were shifted to lower values in comparison to the subjects' formant frequencies detected with inverse filtering. Similar observations were made in a computational model with acoustical excitation by [PERSON] et al. [18] who found that the straightening of the VT led to a formant shift to lower frequencies of less than 5% in the frequency range below 4 kHz. These previous studies with acoustic excitation only indicate that the bend of the VT is acoustically not relevant for frequencies below 4 kHz. This is contrary to the results obtained in this study, which exhibit a mean deviation of 13% between the formant frequencies of the simplified and realistic VT replicas. By including the internal flow, we assume that a change of the flow field in the VT (realistic vs. simplified) leads to a variation of the flow acoustics, which also influences the formant frequencies. Additionally, the opening of the vocal folds, which is induced by the flow, may decrease the reflection coefficient at the glottis and periodically change the acoustic properties of the VT. This effect has so far not been taken into account in acoustic simulations. Another possible explanation for the difference between our results and the results of [PERSON] et al. [18] are differences in the simplification process. Whereas the simplified VT replicas in this study contain between 34 and 37 cross sections, the number of cross sections used by [PERSON] et al. [18] is 80. Furthermore, the differences between the formant frequencies of the realistic and simplified VT replicas of the subjects 3 and 4 are in the same order of magnitude as those found by [PERSON] et al. [18], which are based on a single subject. The difference would arguably be greater if the VT of an additional subject would have been included in that study. In order to elaborate the difference between the resonance properties of the VT replicas and the tenor's VTs, the relative deviations of the four replica formants from the subjects' formant frequencies are depicted in Figure 9. Therein, the mean deviation of the formant frequencies for both, realistic and simplified VT replicas, is 12%, with a range of 1% to 30% for the realistic VTs and a range of 1% to 35% for the simplified VT replicas.