# Calibration of a Quartz Tuning Fork as a Sound Detector
## 2 Materials and Methods  
### Experimental Setup  
Figure 1 shows the experimental setup for the calibration of the QTF. The ultrasonic piezo loudspeaker L010 from Kemo Electronic GmbH (Geestland, Germany), with a membrane diameter of 41 mm, was used to generate an adjustable sound pressure wave. An aperture with an adjustable round opening in the center was placed in front of the loudspeaker to dampen the wave and to achieve a precise alignment in front of the sensors. The acoustic sensor (microphone or QTF, respectively) was placed at a distance of \((2.00\pm 0.05)\) mm, centrally, in front of the opening. The distance between the loudspeaker and the aperture was 3 cm, whereas the dimensions of the aperture plate were \((12\text{ cm})^{2}\).  
The signal generator 33220A from Agilent (Santa Clara, CA, USA) produced the sinusoidal excitation voltage. Respective preamplifiers boosted the sound detector signals,  
Figure 1: Measurement setup.  
while the Lock-In-Amplifier (LIA) Signal Recovery 7265 from AMETEK Scientific Instruments (Oak Ridge, TN, USA) recorded the signal at the excitation frequency with a time constant of 2 s. The entire experiment was controlled by a self-programmed MATLAB (9.14.0.2306882 (R2023a) Update 4) script on a PC.  
The investigated QTF R38-32.768-12.5-EXT-5 PPM from Raltron (Doral, FL, USA) had standard dimensions and a bandwidth of 4.72 Hz [14]. The electronic Q-factor of the QTF in a vacuum is 60,000, according to the manufacturer. Based on our own measurements, we have obtained an acoustic Q-factor of q = 6939 [14] in air. The QTF prongs each have a length of 6.00 mm, a width of 0.65 mm, a depth of 0.30 mm, and a gap of 0.20 mm (measured with microscope Stereo Discovery.V12 from Zeiss, Jena, Germany). The resonance frequency of the QTF of \(f_{R}=32,758\) Hz deviates slightly from the above-mentioned standard frequency (within the manufacturing tolerances). When excited with sound, the oscillations of the QTF generate a small piezoelectric current. This current is converted into an output voltage using a homemade transimpedance amplifier with a feedback impedance of 2.2 M\(\Omega\). The electrical circuit of the QTF transimpedance amplifier is shown in Figure 2.  
The operational amplifier (OPA) 134 PA from Texas Instruments (Dallas, TX, USA) is the central component of the circuit. The typical electrical noise is specified by the manufacturer to be 0.00008% total harmonic distortion plus noise (THD+N). The resulting transimpedance for the circuit is \(Z=-2.2\mathrm{kV}/\mathrm{mA}\). Its gain-bandwidth product (GBP) is 8 MHz, and the THD+N for 32 kHz is less than 0.001%. It is therefore reasonable to assume that the main source of noise is the tuning fork.  
The calibration of the QTF was undertaken using a highly sensitive ultrasonic measuring microphone as a reference sensor. To do so, the QTF in Figure 1 was replaced with the 46 BD 1/4\({}^{\prime\prime}\) CCP microphone set for pressure measurements from GRAS Acoustics (Holte, Denmark). It has a frequency range of 5 Hz to 70 kHz, a dynamic range of 44 dB (A) to 168 dB, and an average sensitivity of 1.45 mV/Pa. We operated it with the standard preamplifier 12 AL 1-Channel CCP Power Module from GRAS Acoustics.