## 3 Results and Discussion
### Numerical Simulation of the Acoustic Wave  
The velocity of the plasma explosion shock wave is close to the speed of sound in the later stage of propagation, and the pressure waveform of the shock wave can be equivalent to the sound pressure. Since most of the energy injected into the plasma channel is used to maintain the occurrence of the corona, generating light and heat, only a small part of it can be converted into acoustic wave energy. In addition, the real air is not ideal gas, and the wave will be partially absorbed by air during propagation. Therefore, the sound pressure conversion efficiency needs to be set to simulate the actual sound source pressure. This paper selects the shock wave pressure waveform at a distance of 10 cm from the plasma explosion point, and it sets the efficiency of converting shock wave pressure to sound pressure to 3%. The time-domain sound pressure waveform of the sound source is obtained in Figure 14.  
The parameters of the acoustic field are as follows: the ambient temperature is 20 \({}^{\circ}\)C, the air humidity is 50%, the density of air is 1.2 kg/m\({}^{3}\), the concrete density is 2300 kg/m\({}^{3}\), the sound velocity in air is 343 m/s, and the sound velocity in concrete is 3000 m/s. The  
Figure 14: Time\(-\)domain sound pressure waveform of plasma explosion sound source. Figure 13: The variation of peak overpressure and shock wave propagation velocity with distance: (a) Peak overpressure; (b) Propagation velocity. sound pressure distribution result at different times is shown in Figure 15. It can be seen that sound waves expand outward in the form of spherical waves, and the amplitude of pressure decreases gradually. When sound waves reach the ground, only a small portion of them pass through the concrete, and most of them are reflected back into the air. The reflection of sound waves is related to the density and sound velocity of materials on both sides of the material interface. The density and sound velocity of concrete are much higher than that of air, and the reflection coefficient is close to 1. Therefore, sound waves undergo reflection at the ground and continue to propagate back into the air. Figure 16a shows the changes in the first sound pressure waveform received at five monitoring points. It can be seen that as the sound wave moves away from the source, the attenuation amplitude gradually slows down. The sound wave decays by 56% from 0.5 to 1 m, while there is only 16% attenuation from 2 to 2.5 m. The changes in the amplitude of pressure reflect the attenuation characteristics of sound waves in space. The changes in the positive and negative peaks of sound pressure with propagation distance are shown in Figure 16b. It can be seen that the positive peak value is always greater than the negative, and the absolute ratio of the two changes is between 1.3 and 1.6. When the wave transforms from the expansion state of the positive half wave to the compression state, it is affected by the viscosity of the air; therefore, the negative half-peak value is lower. The comparison results of the simulation waveform of sound pressure at 2.5 m with the measurement waveform of reference [30] are shown in Figure 17. The simulation results have a higher positive peak value, indicating that the simulation waveform can better reflect the viscosity of the air, which means the difference between the positive and negative peak is greater. The rising edge of the measurement wave is relatively gentle, which may be due to the recovery time of the real air after being influenced by external disturbance being longer. Although there are some differences between the two waveforms, the basic characteristics are the same, proving that the developed method possesses strong applicability and has some room for improvement. Figure 15: Sound pressure distributions of corona noise at different moments: (**a**) 1.14 ms; (**b**) 2.22 ms; (**c**) 3.72 ms; (**d**) 5.97 ms.