# The Influence of Sensor Size on Acoustic Emission Waveforms--A Numerical Study
## 5 Secondary Effects  
The influence of the pulse length or waveform duration is also of interest as it results in a different physical waveform length acting on the sensor's surface. This should not be confused with the wave length which is the wave parameter defined as propagation velocity over frequency. To examine the influence of the waveform duration (i.e., short vs. long signal of the same basic frequency), surface wave simulations were repeated for different number of excitation cycles (from 1 to 20). Two cases of excitation frequencies and sensor sizes were applied, i.e., 1 MHz (wavelength \(\lambda\) = 2.35 mm) with 5 mm sensor size and 500 kHz (\(\lambda\) = 4.7 mm) with 20 mm sensor size. For both cases, one cycle of excitation  
Figure 14: Waveforms received by long size (R15, 20 mm) sensor in the case of (**a**) horizontal surface; (**b**) vertical excitation; (**c**) The average FFT curves of previous waveforms. produces a wavelength smaller than the sensor size, while adding more cycles results eventually in a total wave longer than the sensor size. Indicative waveforms for frequency of 500 kHz received by the 20 mm size sensor for 1 and 10 cycles of excitation are shown in Figure 15a. As the waveform becomes longer, the received peak amplitude increases (see Figure 15a). There is a characteristic point at which a jump in amplitude is observed. This is when the total wave length becomes equal to the sensor size, as seen in Figure 15b. In this figure, the amplitude for each curve is normalized to maximum, while the horizontal axis measures the total waveform length (number of cycles times the wave length) over the sensor size. Therefore, it is seen that the duration of a waveform has an indirect effect on the measured amplitude since when its length becomes equal or longer than the sensor, it can increase the latter by approximately 35%. This influence of waveform length (pulse length) over sensor size is noticeable in the simulation but is not as strong as the wavelength over size influence that was presented in Figure 9. In addition, for experimental waveforms which usually do not have constant amplitude cycles this effect would be weaker due to lower level of constructive interference. The minimum sensor size used in this study as reference was 1 mm. Although this is not exactly a \"point\", or infinitesimally small sensor, the results do not deviate significantly for the casual AE wavelengths. Figure 16 shows the simulated received waveforms for sensors of 1 mm, 0.5 mm and 0.1 mm after a surface excitation of 200 kHz which is typical for AE in concrete. The waveforms are literally identical without distortion on the shape or the peak to peak amplitude. Therefore, considering that element sizes smaller than 1 mm are not commonly used in AE practice, the sensor of 1 mm was considered as reference. Figure 16: Simulated waveforms received by different size sensors from surface source with excitation frequency equal to 500 kHz (curves overlap). Figure 15: **(a)** Simulated waveforms received by 20 mm size sensor after surface source excitation with frequency of 500 kHz and different number of cycles; **(b)** Relative amplitude vs. waveform length over sensor size. A further point that should be kept in mind is related to the dispersion phenomenon. This study focuses on a homogeneous bulk material and monochromatic frequency in order to quantify the sensor size effect. Different cases of media can be considered in the future, like the case of heterogeneous bulk material, where scattering dispersion may impose a frequency dependent velocity as well as the case of thin plates where dispersion originates from the geometry (plate wave dispersion). In these cases, the pulse would spread in time domain altering the duration and the contact time with the sensor. Another interesting case is of anisotropic media where velocity (and thus wavelength) changes with direction, typical of composite plates. There the \"aperture\" effect would change for different directions depending on the orientation of the fibres.