# Numerical and Experimental Investigation of Guided Wave Propagation in a Multi-Wire Cable
## 4 Experimental Analysis
### Single Wire  
In these single wire experiments, four pitch-catch configuration cases were employed for guided wave dispersion verification. The center frequency of the exciting tone burst was 60 kHz. In Case 1, the exciting transducer was installed on the end face of the left end, and the receiving transducer was similarly installed on the end face of the right end. In Case 2, the exciting transducer was installed on the end face of the left end, but the receiving transducer was installed on the lateral face of the right end. In Case 3, the exciting transducer was installed on the lateral face of the left end, but the receiving transducer was installed on the end face of the right end. In Case 4, the exciting transducer was installed on the lateral face of the left end, and the receiving transducer was similarly installed on the lateral face of the right end.  
The representation of a signal in the time and frequency domain can be expressed using a spectrogram. A spectrogram is a time-frequency plot obtained using time-frequency analysis, such as a continuous wavelet transform (CWT). It is a method used to measure experimental group velocity dispersion curves. Figure 12 shows the time-frequency spectrum of the received signals in the four experimental cases using the CWT method, over which the theoretical time-frequency group velocity dispersion curves are overlaid. The theoretical propagation time was calculated using:  
\[t=L/v_{group} \tag{5}\]  
where \(L=1.6\ m\) is the length of the wire and \(v_{group}\) is the group velocities of all existent modes at each frequency between 0 kHz and 100 kHz. This process is equivalent to mapping the group velocity dispersion curves from the velocity-frequency domain to the time-frequency domain.  
There were three guided wave modes in the 7-mm-diameter steel wire below 100 kHz, whose dispersion curves were described in Section 2.1. According to the wave structures plotted in Figure 2d,e, the radial and \(z\)-axial vibration displacements were the main components of the L(0,1) and F(1,1) modes at 60 kHz, respectively. \(Z\)-axial wave components were generated through horizontal excitation of the transducer. Radial wave components were generated through lateral excitation. Similarly, the  
Figure 12: The time-frequency analysis spectrum using a continuous wavelet transform (CWT) for a single 7-mm-diameter steel wire at a 60-kHz frequency: (**a**) horizontal excitation and horizontal reception, (**b**) horizontal excitation but lateral reception, (**c**) lateral excitation but horizontal reception, and (**d**) lateral excitation and lateral reception. The theoretical group velocity dispersion curves obtained in Figure 1a are represented by the dotted line.  
horizontal and lateral reception methods of the transducer effortlessly received the \(z\)-axial and radial wave components.  
Thus, the L(0,1) mode was highlighted in the measured group velocity dispersion nephograms shown in Figure 12a of Case 1. The same applied to the L(0,1) and F(1,1) modes in Cases 2 and 3 simultaneously, and F(1,1) in Case 4 individually. No torsional mode was highlighted in any of the four cases, since neither of the two excitation methods could generate a rotational displacement component.