# Acoustic and Aerodynamic Coupling during
## 1 Introduction  
The human voice results from the flow-induced oscillations of the vocal folds, as described by [PERSON] [1]. This so-called phonatory process is the result of a fluid-structure-acoustic interaction between the laryngeal airflow and the vocal fold tissue. By this oscillation, the basic sound of the human voice is generated which is further transformed in the vocal tract producing the voice signal that radiates from the mouth. Hereby, the vocal tract does not only serve as a downstream resonator, but influences the pressure distribution in the glottal duct or even enhances the vocal fold oscillations acoustically during singing [2]. As the flow field inside the larynx cannot be observed in vivo, experimental and computational models have been developed to investigate the entire phonatory process. Overviews of the existing experimental and computational larynx models are given elsewhere [3; 4; 5; 6; 7]. Beside the aerodynamic and acoustic coupling effects, the main function of the vocal tract (VT) is to serve as an acoustic filter or resonator, respectively. Acoustic resonances are excited in the VT and amplify the sound pressure of the basic sound signal at specific frequency bands, which are called formants. The formant frequencies vary depending on the geometry of the VT, which conditions the acoustical properties of the voice signal for articulated voiced speech [8]. Although up to five formants have been detected for vowels [9], the first two formants F1 and F2 are sufficient to differentiate vowels [10]. In order to investigate the acoustic resonance properties of the VT, it is necessary to extract the geometric shape of the VT. This can be done using medical imaging techniques, which allow a detailed examination of the VT shape during phonation. [PERSON] [11] and [PERSON] [12] determined the geometry of the VT for different vowels by means of X-ray. In recent studies, Magnetic Resonance Imaging (MRI) was used, which provides much higher contrast and resolution. Based on MRI, [PERSON] et al. [13], [PERSON] et al. [14] and [PERSON] et al. [15] presented VT shapes corresponding to different vowels obtained from single subjects. [PERSON] et al. analyzed the VT shape of four professional sopranos [16] and ten professional tenors [17] who sang the vowel /a/ during register transitions. To generate simplified VT models with similar acoustic properties, [PERSON] et al. [13] determined the cross-sectional area as a function of the position along the centerline of the VT. This area function was subsequently used to design straight VT models with circular cross section. Evaluating these simplified models, numerical simulations of the acoustic behavior showed good agreement with small sound samples recorded from the subject. In a recent study, [PERSON] et al. [18] compared VT models of the vowels /a/, /i/, and /u/ based on the data of [PERSON] et al. [15] for different levels of simplification in an acoustic simulation to determine the influence of geometry simplifications on the sound radiation. The results showed only small deviations of the formants in the transfer function being below 5% in the frequency range up to 5 kHz. For higher frequencies, the simplification produces more relevant deviations due to higher order modes [19]. After the development and computational evaluation of the VT shapes, 3D-printed VT replicas were manufactured to examine the acoustic properties of the VT in experiments. [PERSON] et al. [14] used rapid prototyping to build replicas of the VT for five Japanese vowels based on MRI-data. They determined the transfer function of the VT replicas by exciting them with a time-stretched acoustic pulse played by a horn driver in order to provide a database for the testing of numerical analysis methods. The results showed a good agreement with recorded speech, although the formants were shifted to lower frequencies due to the solid walls of the VT replicas [14]. In a similar setup, [PERSON] et al.