## 3 Experiment
### Distance between the Transmitter and the Receiver  
A wave propagates from the transmitter to the base surface (the 1 st leg). The wave is subsequently reflected back, continuing its path until reaching the surface wall (the 2 nd leg), as shown in Figure 3. The 1 st and 2 nd legs generate a sound path (\(SP\)). The skip distance (\(SKD\)) is a term that measures the distance between the point of excitation (beginning of \(SP\)) and the end of the second leg (end of \(SP\)).  
According to [PERSON]'s law, the refraction angle \(\beta_{S}\) is determined by the following equation:  
\[\sin\beta_{S}=\frac{C_{S2}}{C_{L2}}=\frac{3100}{5790}=0.5354\Rightarrow\beta_{ S}=32.4^{\degree} \tag{7}\]  
\begin{table}
\begin{tabular}{c c c c} \hline \hline
**Number** & **Center Frequency f/MHz** & **Detected Depth D/mm** & **Crystal Dimension/mm** \\ \hline
1 & 5 & 1.28 & 10 \\
2 & 2.5 & 2.48 & 10 \\
3 & 1 & 5.98 & 10 \\ \hline \hline \end{tabular}
\end{table}
Table 2: Measurement parameters of the different frequency transducers.  
Figure 3: Distance between the transmitter and the receiver (\(\beta_{S}\): the refraction angle, \(l\): the distance between transmitting transducer and the first receiving transducer, and \(D\): the plate thickness).  
\begin{table}
\begin{tabular}{c c} \hline \hline
**Name** & **Parameter** \\ \hline Tube voltage & 30 kV (fixed) \\ Tube current & 25 mA (continuously adjustable) \\ X-ray type & Ka \\ Target & Mn \\ Focusing area & 4 mm \(\times\) 4 mm \\ \hline \hline \end{tabular}
\end{table}
Table 3: Main parameters of the X-ray stress analyzer.  
The depth of the 304 stainless steel specimens (\(D\)) is 6 mm. The following equation is adapted:  
\[SKD=2\times D\times\tan\beta_{S}=2\times 6\times\tan(32.4^{\lx@math@degree})=7. 62 mm \tag{8}\]  
The length of the surface distance (\(SD\)) is 3.81 mm, which is half that of \(SKD\). The segments \(L_{1}\), \(L_{2}\), and \(L_{3}\) of the \(SP\) in Figure 3 correspond to the 1 st, 2 nd, and 3 rd legs, respectively. \(SKD\), \(SD\), \(L_{1}\), \(L_{2}\), and \(L_{3}\) can be found using trigonometric functions by setting \(\beta_{S}\) as equal to 32.4\({}^{\circ}\). The 1 st leg can be calculated as follows:  
\[L_{1}=\frac{SD}{\sin\beta_{S}}=\frac{3.81}{\sin(32.4^{\circ})}=\frac{3.81}{0. 5354}=7.12 mm \tag{9}\]  
The distance between the transmitter and receiver (\(l\)) depends on the first leg (\(L_{1}\)) and \(SKD\). The received waves for different transmitter-receiver distances are displayed in Figure 4. The number of received waves is proportional to the transmitter-receiver distance. This can be explained by [PERSON]'s law; thus, when the refracted shear waves reflect from the back wall to the front wall, numerous reflected shear waves turn into longitudinal waves. However, the amplitude of the \(\mathrm{L_{CR}}\) wave is inversely related to the transmitter-receiver distance, since a larger distance attenuates the sonic energy. Therefore, the distance between the transmitting probe and the receiving probe should be as large as possible to avoid integer multiples of \(SKD\), so as to achieve accurate identification of \(\mathrm{L_{CR}}\) waves. In this paper, 37.6 mm was selected as the distance from the transmitter to the first receiver and 7.6 mm was selected as the distance between two receivers.  
Figure 4: Received waves for different distances between the transmitter and the receiver (test conditions: frequency of transducers: 5 MHz, diameter of transducers: 6 mm. \(l\): the distance between transmitting transducer and the first receiving transducer, \(L_{1}\) the first leg, \(SKD\): the skip distance).