# Bar-Wave Calibration of Acoustic Emission Sensors
## 3 Results and Discussion
### AE Sensor Response
#### 3.2.1 KRN Sensor
This compares well to the value reported by [PERSON] and [PERSON] [11], who obtained a similarly flat response of approximately 0 \(\pm\) 2 dB between 20 and 900 kHz (relying on theoretical models of capillary break or ball drop). Notice that these results are inapplicable to FET-less KRN sensors [11]. Also note that the NIST conical sensors have \(-\)9 dB theoretical and \(-\)14 dB experimental peak sensitivity [12; 13]. Thus, the FET buffer in these KRN sensors apparently adds about 15 dB gain (when used with a KRN power supply). Figure 6: Output waveform of a KRN sensor (#11063) and its CWT spectrogram for 40–200 \(\upmu\)s segment up to 1 MHz. Some peak positions are marked as cw1 to cw6, which correspond to those in Figure 4.  
Red curves in Figure 8a represent the corresponding velocity sensitivity curves. The velocity receiving sensitivity is given in dB in reference to 0 dB at 1 V output per 1 m/s. Again, the solid one is for the bar-wave sensitivity and dashed for normally incident. Higher frequency dependence is due to spectral differentiation with the multiplication of \(2\pi f\) with \(f=\) frequency. Figure 8b,c show the displacement sensitivity curves for bar waves and normally incident waves of two KRN sensors tested. Red curve is for #11053 and blue curve is for #11063. In these figures, the curves for #11053 were down-shifted 4.4 dB (Figure 8b) and 3 dB (Figure 8c), achieving good matching  
Figure 7: (**a**) The received waveforms on opposite surfaces using a KRN sensor (#11063 with FET buffer) at 300 mm from the transmitter. From 50 to 100 μs; (**b**) Same as (**a**), but for 100–150 μs; (**c**) Same as (**a**), but for 50–350 μs. of the two curves. In Figure 8b, both bar-wave curves rose by 30 dB below 300 kHz, while these were relatively flat from 300 kHz to 1 MHz except for many fluctuations. Many of them are observed at the same frequencies for both. The sensitivities further decreased at >1 MHz. The difference between these two sensors was 4.4 dB on average to 2 MHz (with the standard deviation of 1.46 dB). Figure 8c gives a comparison of displacement sensitivity curves for normally incident waves. The average difference to 1 MHz was 3.0 dB (1.8 dB to 2 MHz); that is, #11053 had a higher sensitivity. These are smoother below 1.2 MHz than the bar-wave responses. Figure 8: (**a**) Receiving sensitivity of a KRN sensor (#11063). The displacement receiving sensitivities are shown in blue curves and velocity sensitivities are in red. Solid lines are for the bar-wave data, while dashed curves are for the sensitivities to normally incident waves; (**b**) Displacement sensitivity curves for bar waves of two KRN sensors: blue for #11063 and red for #11053. The latter was shifted 4.4 dB, giving a good match for the two curves; (**c**) Displacement sensitivity curves for normally incident waves of two KRN sensors: blue for #11063 and red for #11053. The latter was shifted 3.0 dB, giving a good match for the two curves, except above 1.4 MHz. The present results clearly demonstrate that the receiving sensitivities to bar waves and to normally incident waves are different even when the sensing area is small. This confirms that the direction of wave propagation affects sensor response in addition to the well-known aperture effect or waveform cancellation effect [2; 14; 15; 16]. In reference to surface waves, the aperture effect predicts nulls at the zeroes of Bessel function of the first kind, J\({}_{1}\)(ka), where k = 2\(\pi\)/\(c_{\mathrm{R}}\), \(c_{\mathrm{R}}\) = Rayleigh wave velocity and a = radius of the sensor element [2]. The values of ka for the first four nulls, where J\({}_{1}\)(ka) = 0, are 3.832, 7.016, 10.173 and 13.324. In the present case, the wave velocities are those of bar waves and these typically exceed 2 mm/\(\upmu\)s. For KRN sensors, a = 0.5 mm. Thus, the aperture effect has no consequence below 2 MHz. It is expected that a conical element used in NIST-type sensors responds to forces acting at incident angles other than zero. A better analysis of such behavior is desirable.