## 4 Noise Reduction Analysis of the Noise Wall
### Influence of the Noise Wall Height  
Based on the above analysis, the influence of the noise wall height on the noise reduction effect is further investigated, and the noise wall heights are set to be 4 m, 6 m, and 8 m. Figure 11 shows comparisons of 1/3 octave SPLs and insertion losses at six typical field points (N1\({}^{\prime}\)-N5\({}^{\prime}\) and N9\({}^{\prime}\)). Moreover, the equal-loudness-level in \"ISO 226 Acoustic--Normal equal-loudness-level Contours\" [35] is introduced to evaluate the sensitivity of radiated noise in the human ear. In the frequency below 20 Hz, the noise reduction effect of the noise wall works significantly at all points under different noise wall height conditions, and the insertion loss overall increases with the noise wall height, among which the maximum insertion loss of 17.5 dB appears at field point N5\({}^{\prime}\) in the frequency of 10 Hz. The SPLs at all points except point N9\({}^{\prime}\) also decrease with the increase in the noise wall height after setting the noise wall in the frequency range of 20-31.5 Hz, but the overall noise reduction effect changes less with the wall height. The maximum insertion losses at points N1\({}^{\prime}\)-N4\({}^{\prime}\) appear at 25 Hz, which are 12.7 dB, 10.8 dB, 9.0 dB, and 7.8 dB, respectively. For the field point N5\({}^{\prime}\), the SPLs under conditions of 6m and 8 m noise walls are close, the noise reduction effect is significantly enhanced compared to the condition of 4 m noise wall, and the maximum insertion loss exceeds 16 dB. Similar to that in the frequency below 20 Hz, the SPLs of all points decrease with the noise wall height in the frequency range of 40 Hz and above, and all the maximum insertion losses appear in the frequency range of 50-80 Hz, among which all the maximum insertion losses of points N1\({}^{\prime}\)-N5\({}^{\prime}\) all exceed 11 dB, and the maximum value of the point N9\({}^{\prime}\) attains 9.0 dB. According to Refs. [20,36-39], the application of a vibration-damping fastener can reduce radiation noise by 0.5-2.8 dB, and the noise reduction effect of elastomer mats is about 8-23 dB. The above analysis indicates that the noise reduction range of the noise wall at typical points is between 8 and 17.5 dB, which is close to that of structural vibration reduction measures. From the perspective of loudness level, the SPLs of typical field points under noise wall conditions are below the threshold of hearing at the frequency of 25 Hz and below. In the frequency range between 31.5 Hz and 80 Hz, the loudness levels of field points significantly increase with frequency, and the maximum value exceeds 70 phon. In the frequency range above 80 Hz, the loudness levels fluctuate slightly with the frequency within 40-60 phon. Compared with that under the without noise wall condition, the loudness levels under 6 m and 8 m noise wall conditions are significantly reduced in the frequency range of 31.5-80 Hz, and the maximum reduction attains 20 phon at 50 Hz, while the reductions of loudness levels under the 4 m noise wall condition are within 10 phon. To demonstrate the noise reduction effect of the noise wall in the whole sound field, the insertion loss distributions at peak frequencies of the acoustic power, namely 9 Hz, 71 Hz, and 82 Hz, are shown in Figure 12. It can be seen that the insertion loss at the area behind the noise wall and below the deck is overall positive, which represents the noise reduction area, and the others are the noise increase area. As shown in Figure 12a-c, the  
Figure 11: Comparisons of 1/3 octave band SPLs and insertion losses under different noise wall height conditions at field points (**a**) N1\({}^{\prime}\); (**b**) N2\({}^{\prime}\); (**c**) N3\({}^{\prime}\); (**d**) N4\({}^{\prime}\); (**e**) N5\({}^{\prime}\); and (**f**) N9\({}^{\prime}\). insertion losses of the noise reduction area at 9 Hz are small under the 4 m noise wall condition, with a maximum of 4 dB.