# Improving transfer function measurements for three-dimensionally printed waveguides using a sand layer

Rémi Blandin, Patrick Häsner, Peter Birkholz

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Rémi Blandin, Patrick Häsner, Peter Birkholz. Improving transfer function measurements for three-dimensionally printed waveguides using a sand layer. JASA Express Letters, 2025, 5 (2), pp.025203. 10.1121/10.0035803. hal-04980052

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FEBRUARY 07 2025

# Improving transfer function measurements for three-dimensionally printed waveguides using a sand layer

Rémi Blandin ⚙️; Patrick Häsner ⚙️; Peter Birkholz ⚙️

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JASA Express Lett. 5, 025203 (2025)

https://doi.org/10.1121/10.0035803

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# Improving transfer function measurements for three-dimensionally printed waveguides using a sand layer

Rémi Blandin,<fnref n="1" />,<fnref n="2" />,ᵃ) Patrick Häsner,<fnref n="1" /> Ḋ and Peter Birkholz<fnref n="1" /> Ḋ

remi.blandin@univ-rennes.fr, patrick.haesner@tu-dresden.de, Peter.Birkholz@tu-dresden.de

**Abstract:** The reciprocity principle is widely used for acoustic measurements, including three-dimensionally printed waveguide transfer functions. Previous studies revealed unexpected deviations in the 1–4 kHz range, likely due to secondary transmission paths. This study tests the effectiveness of a sand layer in reducing these paths and evaluates measurement variability and robustness to harmonic distortion. The method, tested on an affected replica and two additional replicas, shows that the sand layer effectively minimizes secondary transmission paths. The measurement system proves robust against harmonic distortion, ensuring good reproducibility, with results compared to simulations for validation. © 2025 Author(s). All article content, except where otherwise noted, is licensed under a Creative Commons Attribution (CC BY) license (https://creativecommons.org/licenses/by/4.0/).

[Editor: Douglas D O'Shaughnessy]

https://doi.org/10.1121/10.0035803

Received: 16 October 2024

Accepted: 24 January 2025

Published Online: 7 February 2025

## 1. Introduction

The reciprocity principle, initially defined by Lord Rayleigh (Rayleigh, 1876), is widely utilized in acoustic measurements (Wolde, 2010). In speech acoustics, it helps estimate the transfer function of three-dimensionally (3D) printed vocal tract replicas (Kitamura et al., 2009; Takemoto et al., 2010; Delvaux and Howard, 2014) to analyze vocal tract resonances, including frequency, bandwidth, and amplitude. Fleischer et al. (2018) improved this technique by normalizing with a reference measurement taken in front of the closed mouth of the replicas, addressing non-flat source frequency responses and reducing disturbances like reflections.

Despite the improvements by Fleischer et al. (2018), unexplained artifacts remain in the transfer function estimates of some 3D printed vocal tract replicas. For instance, Fig. 4 from Birkholz et al. (2022) shows unexpected resonances and antiresonances for the vowels /o/ and /u/ above 2 kHz and below 1.5 kHz. These antiresonances, unlikely due to higher-order modes at these frequencies in axisymmetric shapes (Blandin et al., 2015), point to another underlying phenomenon.

A prior experimental study on speech directivity using 3D printed vocal tract replicas also identified unexpected directivity patterns within a similar frequency range (Blandin et al., 2023). This phenomenon was explored by measuring the sound radiated when the mouths of the replicas were obstructed. The study concluded that the observed discrepancies were likely due to secondary transmission paths through the walls of the replicas.

Few studies address the limitations of 3D printing materials for acoustic devices, despite their common use. Research has examined using polylactic acid (PLA) 3D printed material with an infill ratio lower than 100% for sound absorption, with some studies including 100% filled samples as controls (Jiang et al., 2017; Khosravani and Reinicke, 2021; Sekar et al., 2022). The absorption coefficient for these materials ranges from 0.1 to 0.2 at 3–4 mm thickness, higher than that of glass, for example. This suggests that the transmission coefficient may be higher than that of plain materials due to gaps between filaments, making sound transmission through 3D printed walls more important.

Several studies have investigated the use of sand to enhance sound absorption (Indenbom and Pogossian, 2023; Sandu et al., 2023) or attenuate structure-borne sound (Valenza et al., 2009). Its adaptability to various shapes and modular setups, along with its potential to reduce vibration in the vocal tract replica walls, makes it a promising solution for minimizing secondary transmission paths. It was used for this purpose in a previous study (Blandin et al., 2023). However, as previously mentioned, artifacts likely due to transmission through the walls were still observed. This was probably because the entire replicas could not be covered with a sufficiently thick layer of sand due to geometrical

<figure><img src="image_6.png" /></figure>

<footnote n="1">¹Institute of Acoustics and Speech Communication, TU Dresden Helmholtzstraße 18, Dresden, 01069, Saxony, Germany</footnote>

<footnote n="2">²Université de Rennes, CNRS, IETR-UMR 6164, F-35000 Rennes, France</footnote>

<footnote>a) Author to whom correspondence should be addressed.</footnote>
constraints. Therefore, using a sufficient thickness of sand may effectively reduce sound transmission through the walls of vocal tract replicas.

To date, no thorough evaluation has been done on sand's effectiveness in reducing sound transmission through 3D-printed waveguide walls. Additionally, the method proposed by Fleischer et al. (2018) has not been assessed for reproducibility or robustness against harmonic distortion. The method's measurements were compared to simulations only up to 6 kHz, but it relies on simplifying assumptions, such as a uniform acoustic field at the mouth exit. Comparing measurements and simulations at higher frequencies could show if these assumptions cause significant deviations.

Therefore, this study aims to evaluate the effectiveness of using sand to minimize secondary transmission paths through the walls of waveguide replicas and to assess the measurement system's reliability in terms of reproducibility, robustness against harmonic distortion, and consistency with simulations up to 10 kHz.

To achieve this purpose, an experimental setup has been designed to surround vocal tract replicas with a sand layer at least 30 mm thick. The system is tested using a vocal tract replica representing the vowel /u/, where problematic artifacts were previously observed. This method is compared to the original measurement technique and other approaches, such as wrapping the replica in sound-absorbing fabric and placing it in an empty case. The variability of the measured transfer function estimate is evaluated by repeating the measurement three times for each configuration. Finally, the method is also tested on the vowels /a/ and /i/ and compared to simulations.

## 2. Methods

### 2.1 Theory

According to Eq. (A.10) from Kitamura et al. (2009), the acoustic pressure $P_{in}(\omega)$ measured at the glottis of an externally excited vocal tract replica can be related to the volume velocity transfer function $H(\omega) = U_{m}(\omega)/U_{g}(\omega)$, with $U_{m}(\omega)$ and $U_{g}(\omega)$ the volume velocity at the mouth exit and glottis, respectively, through the following relationship:

$$P_{in}(\omega) = \left(1 + \frac{Z_{r}(\omega)}{Z_{0}}\right) P_{s}(\omega) H(\omega), \quad (1)$$

where $Z_{r}(\omega)$ is the radiation impedance, $Z_{0}$ is the characteristic impedance of a plane wave in free space and $P_{s}(\omega)$ is the acoustic pressure of the wave produced by the loudspeaker at the mouth exit.

The innovation of Fleischer et al. (2018) consists of dividing $P_{in}(\omega)$ by the acoustic pressure $P_{s}(\omega)$ measured at the closed mouth exit. It compensates for the sound source's non-flat acoustic response, loudspeaker radiation characteristics, and artifacts like reflections on neighboring objects, resulting in a smoother measured frequency response. However, contrary to the claim made by Fleischer et al., the ratio $P_{in}(\omega)/P_{s}(\omega)$ is not exactly the volume velocity transfer function. Instead, it is proportional to it by a factor $(1 + Z_{r}(\omega)/Z_{0})$, as shown in Eq. (1). Therefore, we refer to it hereafter as the transfer function estimate,

$$\hat{H}(\omega) = \frac{P_{in}(\omega)}{P_{s}(\omega)} = \left(1 + \frac{Z_{r}(\omega)}{Z_{0}}\right) H(\omega). \quad (2)$$

However, as noted by Kitamura et al. (2009), the resonance and antiresonance frequencies remain constant for both the transfer function $H(\omega)$ and its estimate $\hat{H}(\omega)$. Therefore, to prevent mixing experimental data with theoretical predictions, only the transfer function estimate is presented hereafter. For the vocal tract geometries tested, the factor $(1 + Z_{r}(\omega)/Z_{0})$ can cause a maximum deviation of 10 dB from $H(\omega)$ in the range 0–10 kHz. This high value results from the large opening used in the setup, an 18 mm radius, which is a significant size for vocal tract geometries (see Sec. 2.2). Halving the radius would reduce the maximum deviation to about 4 dB within 0–10 kHz.

### 2.2 Experimental setup

The measurement principle is illustrated schematically in Fig. 1(a) with corresponding pictures shown in Figs. 1(b), 1(c), 1(d), and 1(e). The vocal tract replicas were previously constructed for earlier research, with fabrication methods described in Birkholz et al. (2022). The geometry of the replicas was generated using the articulatory synthesizer VocalTractLab (Birkholz, 2013). These replicas have a wall thickness of 3 mm and are 3D printed from PLA with a 100% infill ratio.

A cylindrical case was 3D-printed in black Tough PLA (100% infill) using an Ultimaker 5 to enclose the replicas in a ≥ 30 mm thick grainy sand layer (grain size: 0.47 mm ± 0.22 mm). The case measures 206 mm in length and 122 mm in width, with a wall thickness of 3 mm. It includes a 36 mm diameter hole at the bottom for the mouth opening, and the vocal tract replicas can be inserted into a slightly larger hole just before this opening. This design prevents sand leakage but extends the replicas with a 3 mm long and 36 mm wide cylinder, as illustrated in Fig. 1(a). This extension causes a very slight decrease in the resonance frequencies. However, as discussed in Sec. 3.1, this minimal deviation falls within natural variability. Nonetheless, the extension was included in the simulations in Sec. 3.2.

The measurements were conducted in the anechoic room at TU Dresden, controlled by the software MeasureTransferFunction, which is freely available at vocaltractlab.de.¹ A logarithmic sweep ranging from 100 to 10 000 Hz and lasting 9.92 s was generated and sent to a loudspeaker (VISATON speaker, VISATON, Haan, Germany; type FR 10-8 Ohm in a
<figure><img src="image_7.png" /><figcaption>Fig. 1. (a) Schematic of the experimental setup, (b) vocal tract replica measured alone, (c) vocal tract replica wrapped in sound-absorbing material, (d) global view of the experimental setup with the case containing the replica, (e) case filled with sand.</figcaption></figure>

custom-made cylindrical enclosure) via a sound card (Aureon Xfire 8.0HD, Terratec, Nettetal, Germany). The acoustic pressure $P_{in}(\omega)$ was measured at the entrance (glottis side) of the vocal tract replicas using a microphone (MTG MK301E, AcSoft, Bedfordshire, UK) fitted into a rubber adapter. To measure the acoustic pressure $P_s(\omega)$, the exit (mouth side) of the replica was sealed with a stiff plate. A GRAS 40SC probe microphone (GRAS Acoustics, Holte, Denmark) with an 80 mm probe was positioned as close as possible to the plate, taking care to avoid direct contact between the probe and the plate. The signals of both microphones were transmitted through the sound card to the computer.

Harmonic distortion from the loudspeaker was compensated using the method described by Farina (2000). A Tukey (tapered cosine) window was applied to isolate the linear impulse response from the distortion products. The user manually specified the start and end points of the window's constant central portion, while the rising and falling edges of the window were fixed at a duration of 10 ms each. Additionally, the sensitivity of the microphones and the non-flat frequency response of the 80 mm probe were compensated based on calibration data provided by the manufacturers.

To test various methods for reducing secondary transmission paths, the transfer function estimate $\hat{H}(\omega)$ for the vowel /u/ was measured under different conditions:

* Without any treatment [Fig. 1(b)],

* with sound-absorbing fabric wrapped around [Fig. 1(c)],

* placed in the empty case,

* placed in the case filled with sand [Fig. 1(e)].

Each measurement was repeated three consecutive times, with the replica being unmounted and remounted between each trial, to assess the overall variability of the measurement process and the impact of the different treatments on the variability.

To evaluate the contribution of positioning errors to the overall variability, the vowel /u/ was measured three times in the sand configuration without moving the setup. Additionally, to evaluate the harmonic distortion compensation method, the vowel /u/ was measured three times in the same configuration with sweep amplitude settings of 0.25, 0.5, and 1. The sweep is logarithmic, so changing its time-domain amplitude does not affect all frequencies evenly. However, adjusting the amplitude can still help detect potential non-linear effects.

Finally, to determine the applicability of the approach to different vocal tract geometries, the vowels /a/ and /i/ were measured both with no treatment and with sand. This evaluates the method across the three most distinct vocal tract configurations, capturing the maximum geometric variation with the fewest configurations.

## 2.3 Simulations

The simulations were conducted using VocalTractLab3D (Blandin et al., 2022), which enables precise 3D acoustic simulations of vocal tract geometries. The vowels were modeled as a series of cylindrical tubes, with their parameters derived
from the vowels' area functions using a MATLAB script. These parameters were saved in comma separated values format (CSV) files and imported into VocalTractLab3D to compute the transfer function from the glottis to the center of the exit. Visco-thermal wall losses were taken into account by selecting the option "Visco-thermal losses."

VocalTractLab3D calculates volume-velocity to pressure transfer functions, which are related to the volume-velocity transfer function $H(\omega)$ by the equation $H_p(\omega) = Z_r(\omega)H(\omega)$. Therefore, to convert these transfer functions to the transfer function estimate $\hat{H}(\omega)$, the correction factor is $(1/Z_r(\omega) + 1/Z_0)$, as shown in the following equation:

$$ \hat{H}(\omega) = \left( \frac{1}{Z_r(\omega)} + \frac{1}{Z_0} \right) H_p(\omega). \qquad (3) $$

The radiation impedance $Z_r(\omega)$ is computed using the flat piston radiation impedance (McCord Morse and Ingard, 1986).

## 3. Results

### 3.1 Comparison of different measurement conditions for the vowel /u/

The measured transfer function estimates for four different treatments are shown in Fig. 2, with three repetitions overlaid for each condition. The figure reveals that the artifacts in the 1–4 kHz range are completely eliminated with the use of sand. In contrast, these artifacts are only slightly diminished with the other two treatments. However, when sand is used, the transfer function estimate becomes noisier in the 5–6 kHz range, and a resonance followed by an antiresonance becomes apparent.

In Fig. 2, one can see that the variability is smaller up to 5 kHz when sand is used. To quantify this, the standard deviation of the amplitude across the three measurements for each condition has been computed using the MATLAB (R2021a) functions mean and std. The average and maximum values for the 0–5 and 0–10 kHz ranges for each condition are shown in Table 1. The table indicates a progressive reduction in the average standard deviation for the wrapped, empty, and sand conditions. This reduction is observed in both frequency ranges but is more pronounced in the 0–5 kHz range. A similar trend is observed for the maximum standard deviation, except for the sand condition in the 0–10 kHz range, due to the noisy 5–6 kHz band.

In addition to comparing the amplitudes, resonance frequencies, –3 dB bandwidths, and amplitudes were extracted. To quantify the variability of these parameters, their standard deviation across the three repetitions has been computed. The average standard deviations are provided in Table 2. The average standard deviation is small for all parameters and conditions: approximately 0.2% for the frequencies, 3 Hz for the bandwidths, and 1 dB for the amplitudes. For the sand condition, the standard deviations for the resonance frequencies and amplitudes are slightly lower.

The average resonance parameters for the no treatment, wrapped, and empty case conditions were compared to those for the sand condition, as shown in Table 2. There are no substantial differences between the three conditions and the sand condition, except that the empty case is slightly closer in terms of bandwidth and amplitude. Therefore, there is no measurable reduction in resonance frequencies due to the small extension added by the case.

The variability observed in Fig. 2 and quantified in Tables 1 and 2 is primarily due to small variations in the positioning of the experimental setup elements. To assess this, the sand configuration was measured three times without moving the setup to ensure variability was only from background noise. This approach showed significantly lower variability compared to repositioning the elements between repetitions. The average absolute difference was 0.1 dB, with an average standard deviation of 0.09 dB and a maximum of 3.1 dB in the 0–5 kHz range. The noisy 5–6 kHz band caused slightly higher variability in the 0–10 kHz range, with an average deviation of 0.2 dB and a maximum of 10 dB.

<figure><img src="image_8.png" /><figcaption>Fig. 2. Transfer function estimate of the same replica (corresponding to the vowel /u/) measured under different conditions: without treatment, wrapped in sound-absorbing fabric, placed in an empty case, and placed in the same case filled with sand. The curves for the different conditions are offset by 20 dB to enhance their distinction.</figcaption></figure>
<table><caption>Table 1. Average and maximum standard deviation (in dB) of the measured transfer function estimate of the vowel /u/ across three repetitions for four conditions: no treatment, wrapped in sound-absorbing fabric, placed in an empty case, and placed in the same case filled with sand.</caption><thead><tr><th></th><th></th><th>Nothing</th><th> Wrapped</th><th>Empty case</th><th>Sand</th></tr></thead><tbody><tr><td rowspan="2">0-5 kHz</td><td>Average</td><td>1.3</td><td>0.97</td><td>0.94</td><td>0.39</td></tr><tr><td>Maximum</td><td>20</td><td>19</td><td>4.0</td><td>2.6</td></tr><tr><td rowspan="2">0-10 kHz</td><td>Average</td><td>1.4</td><td>0.85</td><td>1.1</td><td>0.84</td></tr><tr><td>Maximum</td><td>20</td><td>19</td><td>11</td><td>19</td></tr></tbody></table>

To evaluate the efficiency of the signal processing method in compensating for harmonic distortion, the sand configuration was measured at three different amplitude settings. The results from these measurements were very similar. The average absolute amplitude difference was 0.13 dB, with an average standard deviation of 0.10 dB in the 0–5 kHz range and a maximum of 3.5 dB. There was slightly more variability in the 0–10 kHz range, with an average standard deviation of 0.21 dB and a maximum of 8.3 dB. This variability is marginally higher than that observed in the static repetition measurements mentioned earlier, due to one of the measurements being conducted at a lower amplitude than usual.

## 3.2 Comparison with simulations

Figure 3 shows the transfer function estimates, both simulated and measured without treatment and with sand, for the vowels /a, i, u/. The curves show a generally good visual agreement. The resonance parameters indicate a close match for frequencies and amplitudes, with differences of up to 1.4% and 4.2 dB, respectively. However, the bandwidths exhibit greater variation, with differences averaging up to 38 Hz. Above 3 kHz, the bandwidth is consistently higher in the simulations.

Measured and simulated data agree slightly better with sand than without treatment. Except for the 5–6 kHz range, the shape of the sand-treated measurements is closer to the simulations. Without treatment, some resonances show a strongly distorted shape and substantially lower amplitude, such as the second and third resonances of the vowel /i/. For each vowel, unexpected artifacts appear in the 5–6 kHz range of the measurements with sand. The resonance frequencies of both measurements are very close, but the bandwidths of the sand-treated measurements are closer to the simulations (29 Hz instead of 38 Hz). A similar trend is observed for the amplitude of the resonances (3.6 dB instead of 4.2 dB).

## 4. Discussion

Sand effectively reduces transmission through replica walls, except for artifacts in the 5–6 kHz range. The improvements achieved by the other two methods are minimal. The remaining variability is likely due to positioning variations, as indicated by the static repeatability measurements. This improvement in measurement quality is also evident from the better alignment with the bandwidths and amplitudes of the resonance simulations. Overall, the experimental setup is reliable, showing little variation between repeated measurements and robustness to harmonic distortion.

The improvement can be attributed to the reduction of secondary transmission paths, which can substantially impact the measurement when the direct path has a very low amplitude. This is why the 1–4 kHz artifacts are mainly observed with strong constrictions (/u/ and /i/ here, /o/ and /u/ in Birkholz et al., 2022). However, the use of sand also substantially improved the measurements for /a/. The reduction in variability may be because secondary transmission paths are highly sensitive to the positioning of the replicas relative to the sound source.

A similar explanation was proposed in a previous study on speech directivity using 3D printed vocal tract replicas (Blandin et al., 2023). That study found that unexpected directivity patterns in the same frequency range were due to a combination of relatively high transmission through the walls and low transmission through the mouth. This issue predominantly affected vowels /u/ and /i/, which have narrower constrictions. However, in that study, using sand did not prevent the phenomenon, likely due to geometric constraints that prevented sufficient sand thickness around the replicas.

<table><caption>Table 2. Average standard deviation of the absolute differences in resonance frequencies, bandwidths, and amplitudes across four conditions for the vowel /u/: no treatment, wrapped in sound-absorbing fabric, placed in an empty case, and placed in a sand-filled case. Additionally, the average absolute differences relative to the sand-filled case are provided for comparison. For resonance frequencies, differences are calculated relative to the average values or the sand-filled case.</caption><thead><tr><th rowspan="2"></th><th colspan="4">Standard deviation</th><th colspan="3">Difference with sand condition</th></tr><tr><th>Nothing</th><th> Wrapped</th><th>Empty case</th><th>Sand</th><th>Nothing</th><th> Wrapped</th><th>Empty case</th></tr></thead><tbody><tr><td>Frequency (%)</td><td>0.17</td><td>0.22</td><td>0.17</td><td>0.13</td><td>0.21</td><td>0.46</td><td>0.32</td></tr><tr><td>Bandwidth (Hz)</td><td>2.0</td><td>2.9</td><td>2.9</td><td>2.1</td><td>3.4</td><td>3.3</td><td>1.6</td></tr><tr><td>Amplitude (dB)</td><td>0.90</td><td>0.70</td><td>0.72</td><td>0.65</td><td>1.8</td><td>1.7</td><td>0.5</td></tr></tbody></table>
<figure><img src="image_9.png" /><figcaption>Fig. 3. Transfer function estimates measured without treatment and with sand and simulated with the vocal tract geometries corresponding to the vowels /a/, /i/, and /u/. The curves for the different conditions are offset by 30 dB to enhance their distinction.</figcaption></figure>

This indicates that such problems can occur in direct measurement scenarios and are not specific to reciprocity principle-
based measurement paradigms.

The absorbing material slightly reduces wave amplitude on the replica wall but is less effective in this setup, as it
works best with longer wave paths such as multiple reflections on the walls of a room, or in an enclosed space. However,
it does not address vibrations in the wall itself. Reflection on a hard, heavy surface, like the empty case, is more effective
for reducing transmission. However, the case's open top limits its ability to block waves from all directions. Sand combines
the benefits of added mass and sound absorption, particularly at low frequencies, while also dampening vibrations and
fully surrounding the replica.

The artifacts observed in the 5–6 kHz range are not well understood. One possible explanation is that reducing sec-
ondary paths could lead to a lower amplitude of P<sub>m</sub> if the direct path has a very low amplitude. This might decrease the sig-
nal-to-noise ratio, thus, explaining the noisier data in this frequency range. Additionally, for /u/, an unexpected resonance fol-
lowed by an antiresonance suggests the presence of a transverse resonance (Blandin et al., 2015). The first higher-order mode
has a cut-off frequency of 5.83 kHz, which falls within this range, though it does not exactly match the observed antiresonance.
A transverse resonance could be triggered by a non-uniform incident field or asymmetries in the experimental setup. This
could be further investigated by measuring the incident acoustic pressure at various points around the replica’s exit.

On the other hand, the wavelength in the 5–6 kHz range is roughly equal to the radius of the case, about
60 mm. This suggests that a resonance could occur in the space between the replica and the case. Indeed, sand does not
completely eliminate resonances, as demonstrated by research on Helmholtz resonators filled with sand (Indenbom and
Pogossian, 2023; Sandu et al., 2023). This phenomenon warrants further investigation to gain a better understanding.

The simulations demonstrate good agreement with measurements in the sand configuration and somewhat less
with the no-treatment configuration. This level of agreement is similar to that reported by Fleischer et al. (2018), though
achieved using a different simulation method (multimodal vs finite elements) and across a broader frequency range, up to
10 kHz. This demonstrates that, despite the simplifying assumption of a uniform field over the mouth exit, the method
aligns well with theoretical predictions even at relatively high frequencies. This reinforces confidence in both the measure-
ment technique and the multimodal method implemented in VocalTractLab3D. However, the broader bandwidths
observed above 3 kHz suggest that the loss model slightly overestimates high-frequency losses. This could be improved by
refining the loss model, or it may be that the model is not fully applicable to 3D printed materials. Comparing with other
materials could help clarify this issue.

**5. Conclusion**

The use of a sand layer around vocal tract replicas is an effective and straightforward method to reduce secondary trans-
mission paths. It is inexpensive, easy to implement, and compatible with existing replicas. The experimental setup has
proven to be reliable in terms of repeatability and robustness to harmonic distortion. However, phenomena occurring in
the 5–6 kHz range, such as lower signal-to-noise ratio and unexpected resonances and anti-resonances, are not well under-
stood and require further investigation. More generally, this study highlights the need for caution when using PLA 3 D-
printed material to construct acoustic elements.

**Acknowledgments**

This study was funded by the German Research Foundation (DFG), Grant No. BI 1639/9-1, and by the German Federal Ministry of Education and Research (BMBF) within the project “Promise-AI,” Funding Code No. 16SV8988. The authors sincerely appreciate Jihyeon Yun’s support during the measurement process and for her assistance with proofreading.
Author Declarations

Conflict of Interest

All authors declare that they have no conflicts of interest to disclose.

Data Availability

As described in Secs. 2.2 and 2.3, the vocal tract geometries and simulations were generated using VocalTractLab3D, a freely available tool accessible at https://vocaltractlab.de/.

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