## 2 Experimental Research
### Sound-Simulated Vibrations of the Round Window Membrane  
Figure 2 shows the measured resonance amplitudes at the SF and the RWM and highlights the differences between the closed (blue curve) and open (red curve) artificial external ear canal setups. The artificial ear canal used in the experiment was a cylindrical shape tube of \(l=27.0\) mm length. The natural frequency \(f_{n}\) of the sound wave in this section can be calculated according to the formula  
\[f_{n}=\frac{n\ v}{2\ \beta\ l}\]  
where \(v\) is the sound wave velocity (343 m/s at the room temperature), \(l\) is the tube length, \(n\) is harmonic number, and tracker \(\beta=1\) and \(\beta=2\) for the both ends closed and open-closed ends setups, respectively. Figure 1: Scheme of experimental setup used in experiment on temporal bone. Thus, the fundamental frequency for the open ear canal is approximately 3180 Hz. This is confirmed by the peak of the red solid line representing the RWM frequency plot. The corresponding dashed line peak (SF) is shifted towards higher frequencies (approx. 4100 Hz). This difference may be explained by the fact that the SF response does not include any contribution from the cochlea. The peaks on this line (red dashed) observed at lower frequencies (approx. 1350 Hz and 670 Hz) are its subharmonics. For the closed-closed ends setup (ear canal closed) the natural frequency of the tube canal is about 6360 Hz. The corresponding frequency plots for the SF and the RWM are plotted in blue dashed and solid lines, respectively. The corresponding subharmonic peaks can be clearly observed for both characteristics, but with some notable differences. In particular, there is a strong subharmonic peak at about 670 Hz for the RWM, but its counterpart on the SF plot is much less pronounced. On the contrary, there is a subharmonic peak at about 1400 Hz for the SF characteristic, but no amplification for the RWM line. Another general observation is that, similarly to the open tube setup, the frequencies corresponding to the SF are slightly shifted towards higher frequencies when compared to the RWM ones, which is clearly observed in the 3-4 kHz zone. Again, this is related to the fact the measurements are taken in different locations (SF and RWM), and in the former case there is no contribution of the cochlea. These findings are similar, though not identical, to those reported by [PERSON] et al. [11] and [PERSON] et al. [7]. Specifically, in [11], the primary resonance occurred at 2 kHz, and a smaller resonance occurred at 1 kHz. In contrast, Ref. [7] reports resonances at 500 Hz, 800 Hz, 1.5 kHz, and 5 kHz from experimental data, and at frequencies 750 Hz, 1.4 kHz, and 5 kHz in finite element (FE) model simulations. Therefore, the results from the current research are more consistent with the findings of [7]. The differences between our measurements and those reported in the literature can be attributed to variations in the source and storage conditions of temporal bone specimens across laboratories, individual anatomical differences, and discrepancies in the mass of the retro-reflective markers used in the experiments. The observed disparities between the SF and RWM responses provide general information about the cochlea's characteristics. However, some deeper insights can be obtained while studying the ratio of FRFs measured for the RWM (Equation (3)) and for the SF  
Figure 2: RWM vibration and stapes footplate (SF) vibration as frequency response functions for open (red) and closed (blue) artificial ear canal. (Equation (2)), represented by the \(H_{TV(RWM)}/H_{TV(SF)}\) quotient. These results are plotted in Figure 3.  
In the open canal configuration in the frequency range 0.9-1.8 kHz, the RWM vibration is about two times higher than that of the stages footplate naturally fixed to the OW. The signal amplification is the highest at about 0.95 kHz (about 2.2) and 1.3 kHz (approx. 2.3). For the closed canal, two frequency zones of \(HTV_{(RWM)}/HTV_{(SF)}\) ratio amplification are observed.