# Comparison of the Sensitivity of Various Fibers in Distributed Acoustic Sensing
## 4 Discussion  
To compare theoretical estimates with experimental data, the integral sensitivity \(S_{i}\) of the tested fibers was calculated as follows:  
\[S_{i}=\int\limits_{f_{\rm min}}^{f_{\rm max}}A(f)df \tag{8}\]  
where \(f_{\rm min}\) is the lowest frequency in the range under consideration, \(f_{\rm max}\) is the highest frequency, \(A(f)\) represents the frequency-dependent amplitude of the detected signal for a given FUT (Figure 7), \(df\) is the sampling interval in the frequency domain. In this study, based on the FFT sampling rate, \(df\) was 48.8 Hz. The integral acoustic sensitivity of the FUTs across the entire range of test signal frequencies, as well as for the range from 4500 to 7000 Hz, is presented in Table 3.  
From Tables 2 and 3, theoretical and experimental rankings of the FUTs based on their acoustic sensitivity value can be made (Table 4). Overall, the estimated and experimental results align closely, with some exceptions. \"Fiber 7\" and \"Fiber 3\" displayed lower-than-expected sensitivities across the entire frequency range, whereas \"Fiber 3\" showed higher sensitivity than estimated in the 4500 to 7000 Hz range. Notably, \"Fiber 3\" and \"Fiber 7\" produced very similar response curves (Figure 8a), especially below 4500 Hz. This similarity is likely due to inner strain: \"Fiber 3\" \begin{table}
\begin{tabular}{c c c c} \hline \hline \multirow{2}{*}{**No. pos.**} & \multirow{2}{*}{**Estimated**} & **Experimental (Full \(f\) Range)** & **Experimental** \\ \hline
1 & “Fiber 7” & “Fiber 5” & “Fiber 7” \\
2 & “Fiber 5” & “Fiber 4” & “Fiber 5” \\
3 & “Fiber 4” & “Fiber 1” & “Fiber 4” \\
4 & “Fiber 1” & “Fiber 6” & “Fiber 3” \\
5 & “Fiber 6” & “Fiber 7” & “Fiber 1” \\
6 & “Fiber 3” & “Fiber 2” & “Fiber 6” \\
7 & “Fiber 2” & “Fiber 3” & “Fiber 2” \\ \hline \hline \end{tabular}
\end{table} 
Table 4: FUTs’ rankings based on their estimated and experimental sensitivities (from highest to lowest). \begin{table}
\begin{tabular}{c c c} \hline \hline \multirow{2}{*}{**FUT Designation**} & **Integral Sensitivity \(S_{i}\), rel.** & **Integral Sensitivity \(S_{i}\)** \\  & **Units** & **(4.5-7 kHz), rel. Units** \\ \hline “Fiber 1” & 7,350,248 & 903,327 \\ “Fiber 2” & 6,084,077 & 708,699 \\ “Fiber 3” & 5,215,782 & 948,519 \\ “Fiber 4” & 8,118,668 & 999,861 \\ “Fiber 5” & 10,066,302 & 1,387,439 \\ “Fiber 6” & 6,596,713 & 889,326 \\ “Fiber 7” & 6,143,962 & 1,926,941 \\ \hline \hline \end{tabular}
\end{table} 
Table 3: Integral sensitivity of the FUTs. may experience uncontrolled strain during coating, as copper has a higher coefficient of linear thermal expansion than optical fiber glass. \"Fiber 7\" inherently contains controlled strain due to its borosilicate rods, giving it an anisotropic, polarization-maintaining core. This anisotropy may explain the relatively low sensitivity of \"Fiber 7\" at frequencies below 4500 Hz, as these are the primary features distinguishing it from the other fibers. While one might expect \"Fiber 7\" to show higher sensitivity than \"Fiber 1\" (since both have the same coating type and \"Fiber 7\" has a smaller diameter), the experimental data suggest that the internal strain exerts a greater influence on acoustic sensitivity, potentially contributing to the fiber's frequency-independent sensitivity. This characteristic could be advantageous in DAS applications that require accurate signal frequency spectrum reconstruction, such as sound source identification or distinguishing multiple sound sources, based on \"frequency patterns\" specific to particular sounds--whether they are from wind, vehicles, animals, birds, or intruders. Relevant applications include early pest detection [46], bee monitoring [47], perimeter security [48], pipeline [49], crop [21], and railway [50; 51; 52] monitoring, nondestructive testing [53] and sound design [54]. The exceptional performance of \"Fiber 5\" likely results from two factors. First, coating inhomogeneities appear to resonate with multiple acoustic frequencies in the test signal.