# Calibration of a Quartz Tuning Fork as a Sound Detector
## 3 Results
### Microphone and QTF Detection Limit  
The results of the background noise levels raise the question of whether the microphone exhibits a better detection limit than the tuning fork when acoustically stimulated at the QTF resonance frequency. Therefore, a sound signal, as low as possible, was generated with the loudspeaker behind the aperture and then successively increased.  
Figures 7 and 8 show the signal of the QTF and microphone, respectively, as functions of the sound pressure at the location of the sensors. Both graphs cover the range between 0.330 and 0.596 mPa. This corresponds to loudspeaker voltages between 0 and 5 V, whereas the signals at a loudspeaker voltage of 0 V are in accordance with the RMS of the background signals from the previous measurements. They are shown as dashed lines, while the 95% percentile of the noise are marked with dash-dotted lines.  
Figure 8: Microphone signal as a function of sound pressure (low levels).  
Figure 7: QTF signal as a function of sound pressure (low levels).  
The investigated sound pressure range corresponds to levels between 24 and 30 dBSPL, which is well below the specified limit for the microphone set with a preamplifier of 44 dB (A). However, with the help of the LIA, it was possible to clearly measure a linear signal increase with an increasing pressure level. For the QTF, \(R^{2}\mathrm{QTF}=92.89\%\), while for the measuring microphone, \(R^{2}\mathrm{Mic}=82.49\%\).  
The signal-to-noise-ratio (SNR) in dB is defined as the difference between the signal level and the background noise, both in dB. For the QTF, the highest SNR, based on the linear fit in Figure 7, is 17.58 dB, whereas for the microphone in Figure 8, it is 3.84 dB. The same sound pressure level leads for the QTF, therefore, to a higher SNR compared to that of the microphone. Although the QTF has a larger standard deviation for repeated measurements at a single measurement point, it has a higher sensitivity and SNR for an acoustic signal at \(f_{R}\).  
The detection limits of the microphone and the QTF can be determined from their sensitivities, \(S\), and the standard deviations of the background signal, \(\sigma\).  
\[x=\Phi_{n,\alpha}\frac{\sigma}{S} \tag{3}\]  
The factor \(\Phi_{n,\alpha}\) results from the significance level \(\alpha\) and the number of the measured values \(n\). For a significance level of \(\alpha=0.5\) and four measurement repetitions, \(\Phi_{n,\alpha}=2.6\)[17]. The standard deviation of the baseline measurement \(\sigma\) corresponds to the mean standard deviation of the background signal from Section 3.3, and the sensitivities from Sections 3.1 and 3.2, respectively, lead to the following detection limits for the microphone and the QTF:  
\[x_{\mathrm{Mic}}=2.6\cdot\left(\frac{3.3133\cdot 10^{-8}\ \mathrm{V}}{1.0277 \frac{\mathrm{mV}}{\mathrm{Pa}}}\right)=8.3824\cdot 10^{-5}\ \mathrm{Pa}\,\]  
\[x_{\mathrm{QTF}}=2.6\cdot\left(\frac{4.7386\cdot 10^{-7}\ \mathrm{V}}{6.4737 \frac{\mathrm{mV}}{\mathrm{Pa}}}\right)=1.9031\cdot 10^{-4}\ \mathrm{Pa}\.\]  
The detection limit of the microphone is lower than that of the QTF by approximately a factor of 2.