# Calibration of a Quartz Tuning Fork as a Sound Detector
## 4 Discussion  
The performance of the QTF as a sound detector was investigated and compared to a highly sensitive measuring microphone. The investigation revealed several distinct advantages and limitations for each sensing device. Table 1 shows the results in direct comparison. \begin{table}
\begin{tabular}{l l c c} \hline \hline
**Parameter** & **Unit** & **Microphone** & **QTF** \\ \hline Bandwidth & Hz & \(5\ldots 70,000\) (\(\pm 2\) dB) & 4.72 (FWHM) \\ Dimension & mm & \(53\times 7\) & \(6\times 3\) \\ Price (ca.) & Euro & (incl. preamplifier) & (length \(\times\) width) \\ Sensitivity \(S(f_{R})\) & mV/Pa & 1.03 & 6.47 \\ Linearity of resp. \(R^{2}\) & \% & 82.52 & 92.89 \\ at low level & \% & 100.00 & 99.97 \\ Linearity of resp. \(R^{2}\) & \% & 4.86 & 15.15 \\ Detection limit \(x\) & Pa & \(8.38\times 10^{-5}\) & \(1.90\times 10^{-4}\) \\ SNR at 0.596 mPa & dB & 3.84 & 17.58 \\ \hline \hline \end{tabular}
\end{table} 
Table 1: Key parameter for microphone and QTF in comparison. In summary, the microphone offers sound detection over an extremely wide frequency range. The QTF, on the other hand, is limited to its resonance frequency. A microphone is therefore recommended for all applications that require sound detection at multiple frequencies or over a frequency range. There are also MEMS microphones suitable for the ultrasonic range [18]. Within its resonance band, the QTF, however, is extremely sensitive to acoustic stimulation. It exhibits a higher SNR at a given sound pressure than the measuring microphone, although the QTF's background noise relative to its RMS is higher than that of the microphone. However, since the QTF features a higher sensitivity, its linearity of response and detection limit is comparable with the microphone. This makes the QTF particularly suitable for detecting weak signals at its ultrasonic resonance frequency, which is interesting for applications such as PA spectroscopy or PA imaging [14]. The fact that the detection limit of the microphone is better than that of the QTF but the SNR is significantly lower seems contradictory. However, this is easily explained because the QTF shows a faster increase in SNR after reaching its detection limit  
A particularly notable advantage of QTFs is their cost-efficiency. They are approximately four orders of magnitude less expensive than measuring microphones. Furthermore, their compact dimensions make them ideal for use in small setups. Both properties suggest the use of QTFs for applications aimed at mass production and cost optimization that tolerate the bandpass limitations. Manufacturing tolerances causing slight variations in resonance frequency in QTFs can be easily addressed through simple calibration measurements enhancing the practicality of QTFs for targeted applications [19]. This variability is less impactful in tunable frequency systems but could limit fixed-frequency applications. To further enhance the performance of the QTF, the utilization of sophisticated amplifiers, exhibiting superior SNR characteristics in comparison to transimpedance amplifiers, can be employed [20; 21]. In a standard substitution calibration, sensors of the same type are compared with one another. However, the QTF presents a unique challenge due to its different surface and vibration characteristics compared to the microphone. This discrepancy in excitation surfaces could result in the signal from the QTF rising to a higher relative extent than the signal from the microphone, even though the sound intensity is identical. This could be of additional benefit for applications with particularly low levels as it increases the SNR. Conceptualization, J.F. and M.W. ; methodology, J.F. and M.W. ; software, J.F. ; investigation, J.F. ; resources, J.F. ; writing--original draft preparation, J.F. ; writing--review and editing, M.W. ; visualization, J.F. and M.W. ; supervision, M.W. All authors have read and agreed to the published version of the manuscript. This research received no external funding. Not applicable.