# Calibration of a Quartz Tuning Fork as a Sound Detector
## 1 Introduction  
In their standard formation, quartz tuning forks (QTF) are two silica (silicon dioxide) prongs that are connected at one end. This creates a resonator whose resonance frequency is determined by the geometry and the properties of the piezoelectric material. With standard dimensions, their resonance frequency is 32,768 Hz. They are commonly used as the time-frequency standard in watches and digital electronics [1, 2].  
However, the reverse piezoelectric effect results in the generation of electrical charges via the deformation of the crystalline structure. This allows us, for instance, to measure soundwaves at the QTFs resonance frequency. Since QTFs are small and inexpensive compared to measuring microphones and have a highly selective frequency response, they represent a compelling option for applications that undertake acoustic measurements at a fixed frequency. One example of such an application is quartz-enhanced photoacoustic spectroscopy (QEPAS). This technique employs QTFs as detectors for the photoacoustic signal and enables laser spectroscopic gas sensors with extraordinarily high detection sensitivity [3, 4, 5]. The most common configuration is the on-beam configuration, which involves guiding the laser beam centrally through the gap in between the QTF prongs. On the other hand, there is the so-called off-beam configuration, in which the light does not pass through the prongs. The QTF is typically located outside a resonance tube, with a narrow opening in the center. In recent years, there has been a notable increase in the application of QTFs in QEHowever, their response to pressure waves has, so far, not been properly characterized. Several articles on QEPAS demonstrate QTFs' high detection sensitivity, but this usually concerns the concentration limit of trace gases and not pressure levels [9; 10; 11]. Manufacturers provide only the QTF's frequency response (voltage or normalized value over frequency). One approach to measuring the sensitivity of a QTF as voltage per \(\upmu\)m deflection was based on measurements with an atomic force microscope [12]. However, since the actual deflection is usually unknown, it is difficult to relate the results to pressure levels. Another approach used coulometry and delivered the sensitivity of a QTF as resonance frequency change over charge, which was used to determine the mass-charge relationship for electrochemical processes [13]. Unfortunately, this is not directly relevant for acoustic measurements.  
In this study, we calibrated a standard QTF for the first time, applying the well-established substitution calibration method to relate its response to an actual sound pressure level. We used a highly sensitive ultrasonic measuring microphone as a reference sensor. This allows us to determine the QTFs acoustic detection sensitivity, the linearity of its response, and its limit of detection. For the latter, the noise of the sensor and its amplifier was measured.  
The following Section 2 describes the experimental setup and the measurement methods. Section 3 presents the results of this investigation. The characterization of the microphone used is followed by a calibration of the QTF and, successively, a comparison of the level-dependent performances of the microphone and QTF. A discussion of the results concludes this article.