# Acoustic and Aerodynamic Coupling during
## 3 Results and Discussion
### Analysis of the Formant Frequencies
Thereby, the deviations of F1 are less than 5% for both replica versions of subject 4, subject 5, and subject 6 whereas subject 1, subject 2, and subject 3 show larger deviations. On average, the formant frequencies of the realistic VT replicas are shifted to lower frequencies in comparison to the subjects' formant frequencies, as depicted in Figure 7. We suppose that the deviations of the formant frequencies of the realistic replicas in comparison to the subjects' formant frequencies are due to the rigid walls of the VT replicas. This effect of a frequency shift to lower frequencies at rigid walls compared with reflection at tissue was also reported by [PERSON] et al. [55] and [PERSON] et al. [14]. Another possible explanation for the appearing deviations are potential inaccuracies of the VT air volume due to the segmentation process. Nevertheless, the filter properties of both VT types are reproduced in an acceptable range, since a vowel formant is not characterized by a discrete frequency, but by a frequency band [56]. Hence, the simplification of the VT in our replica setup shows a good validity regarding this basic formant characteristics. This finding is similar to other studies [13; 18]. As the generation of the formant frequencies depends on the gradient of the reflection coefficient, we analyzed the reflection coefficients of the simplified and the mean VT replica, see Figure 8.  
Figure 8: Reflection coefficients of the mean and individual simplified VTs as a function of distance to glottis. The geometries for the VT replicas were obtained according to the method described in Figure 2 and Section 2.1. Figure 7: Formant frequencies of the realistic and the simplified VT replicas based on the MRI-data by [PERSON] et al. [34] originating from six tenors singing the vowel /a/. Additionally, the subjects’ formant frequencies are plotted as detected by [PERSON] et al. [34] from audio recordings. The applied detection method for all formants is based on inverse filtering, as described in Section 2.3. It shows that the slopes of the reflection coefficient are similar for the simplified replicas of all subjects. Furthermore, the reflection coefficients of the individual VT replicas are well reproduced by the reflection coefficient of the mean VT replica with increasing distance to the VT inlet. Only in the region between 8 and 10 cm, deviations up to 100% occur. These deviations are produced by the uvula, which is subject to large geometrical inter-individual differences. It is visible that for subject 1, subject 4, subject 5, and subject 6, the reflection coefficient in this area is larger than for subject 2, subject 3, and the mean VT replica due to a more pronounced constriction of the VT. However, no correlation between the degree of the VT narrowing and the formant frequencies of the simplified VT replicas can be observed. The formants of the mean VT replica exhibit a mean deviation of 8% from the average of the subjects' formant frequencies, with a deviation of 10% for F1 and 3% for F2, as depicted in Figure 9. The detected formant frequencies of the mean VT are plotted in the formant chart in Figure 10, as proposed by [PERSON] and [PERSON] [56], in addition to the subjects' formant frequencies. The chart shows F1 and F2 for different vowels, since the speech identification of a certain vowel depends mainly on the first two formant frequencies [10]. The subjects' formant frequencies are all located within the same frequency range, although F1 is shifted to lower frequencies towards the vowel /u/. This shift originates from the fact that professional singers tune their vowels to a darker voice quality, as described by [PERSON] [57]. A classification of F3 and F4 is done based on literature values for men by [PERSON] [58], [PERSON] et al. [13] and [PERSON] [9]. The values of F3 are in the range of 2440 Hz for a spoken /a/[58] and in the range of 2700 Hz for a sung /a/[9]. According to [PERSON] [9], F4 is in the order of 2750 Hz for a dark voice quality and about 3150 Hz for a light voice quality.