# The Spec-Radiation Method for Layered Fluid Media
## 2 Material and Methods
### Experimental Setup  
This experimental setup (see Figure 4) allows the measurement of a sound field emitted by an ultrasonic transducer. The original purpose is the detection of flaws in a particleboard; hence, such a board can be placed in between the sound source and the sensor. Air was used as the coupling medium between the particleboard and the receiver/transmitter. An ultrasonic transducer called AT50 from the company Airmar was used as a transmitter. It  
Figure 3: Flowchart of the block “Interface j” for the practical realization of the spec-radiation method for layered fluid media.  
has an active diameter of 45 mm and operates at 50 kHz. The small frequency allows large distances between the particleboard and the receiver / transmitter. However, the accuracy is lower than with higher frequencies. In air the wavelength was at 50 kHz approximately \(\lambda=6.9\) mm. Thus, due to the theory for the spec-radiation method, the smallest detectable size in air was \(\lambda/2=3.45\) mm. An amplitude of 100 V operates the transmitter to send out a burst of 10 sinusoidal periods with a repeating frequency of 1 Hz. With a distance of 280 mm from the transmitter to the particleboard, the distance was always larger than the near-field length (approximately 72 mm according to [PERSON] and [PERSON] [7]) of the transmitter in air at this frequency. The transmitter was stationary during the whole measurement. As a sample, a commercially available wooden medium-density fiberboard (MDF) was used.  
The particleboard had a thickness of 25 mm. To determine the longitudinal speed of sound in the particleboard, a contact through transmission test was carried out with 50 kHz and was determined to be 450 m/s. The density of the particleboard was 730 kg/m\({}^{3}\). As flaw imitations, pieces of paper were used ([PERSON] et al. [32], [PERSON] et al. [33], [PERSON] and [PERSON] [35], [PERSON] and [PERSON] [47], [PERSON] et al. [30], [PERSON] et al. [28]) due to the similar material properties compared to wooden particleboard. Other studies often use Teflon tape for studying CFRP or GFRP material for the same reason ([PERSON] [3]). When the piece of paper was placed with tape underneath the particleboard, a thin air film was always present, and this film served as the flaw imitation. It caused a similar impedance change as real air inclusion in the material. The two pieces of paper used as the flaw imitation were circular with a diameter of \(\phi\)10 mm and \(\phi\)6 mm, which is larger and smaller than the wavelength of 9 mm in the particleboard, but larger than the half-wavelength. The particleboard was also stationary. As a receiver, a MEMS microphone (SPU0410 LR5H-QB Knowles) was used. Its upper frequency limit is 80 kHz. The receiver had a constant distance of 177 mm from the particleboard. The receiver could be moved to obtain the information for C-scans. Therefore, the XYZ-traversing stage from RoboCylinder with the traverse path of \(x=0\)-400 mm, \(y=0\)-200 mm, and \(z=0\)-200 mm was used. To control the entire system, a standard computer was used. Via USB, the XYZ stage was connected to the computer and controlled by a LabView program. With a National Instruments (NI) system, the transmitter was controlled and the signal of the microphone recorded. The NI system consisted of a chassis PXIe-1085, with an inserted card for the communication with the computer (PXIe-8398), a card to record the measurement data (PXIe-5171R with a maximum sampling frequency of 250 MHz and 8 channels), and a card (PXIe-5423) as a frequency generator to control the transmitter. For the amplification  
Figure 4: Experimental setup.  
of the control signal of the transmitter, the power amplifier HSA 4052 from the company NF was used to generate the required amplitude of 100 V. The measured area had a size of \(152\) mm \(\times 152\) mm with a measurement point distance of 2 mm in \(x\) and \(y\). Hence, \(76\times 76\) points were measured, and the time step was \(2\times 10^{-7}\) s with a time length of \(3.2768\times 10^{-3}\) s.