## 3 Numerical Analysis
### Calculation Results
The difference is small when the additional source is located at 0.3 m and 1 m above the ground. According to the calculation results shown in Figure 3, taking the value of the SPLs near 120\({}^{\circ}\) as the main concern, the ideal locations of the additional source at each frequency can be acquired as shown in Table 1. As can be seen in Table 1, to acquire good performance in multiple frequency bands, the additional source should be located at 0.3 m above the ground. It can also be concluded that good noise reduction can be achieved in a large space when the additional source is located lower than the primary source. Figure 2: Calculation results of sound field when the additional source is located at different locations (800 Hz). source is located at 0.5 m above the ground, but the difference is small compared with when the additional source is located at 1 m above the ground. The SPLs are the smallest in the region of 125\({}^{\circ}\) to 180\({}^{\circ}\) when the additional source is located at 0.3 m above the ground. At the frequency of 800 Hz, in the region of 0 to 150\({}^{\circ}\), the SPLs are almost the same when the additional source is located at 0.3 m and 1 m above the ground and greater than when the additional source is located at 0.5 m above the ground. At the frequency of 1000 Hz, the difference in SPLs is small when the additional source is located at 0.3 m and 1 m above the ground. The SPLs are the smallest in the region of 0 to 150\({}^{\circ}\) when the additional source is located at 0.3 m above the ground. On the whole, it is beneficial to acquire good performance in large spaces behind the barrier when the additional source is located 0.5 m above the ground in the case of the primary source is located at 1 m above the ground. Comparing the calculation results mentioned above, it is clear that the optimal location of the additional source is not the lower the better, but it should be lower than the primary source. Figure 4: Directivity of the sound field over the barrier when the primary source is located at 1 m above the ground. Directivity Calculation When the Primary Source Is Located Away from the Barrier and Double Sources  
Generally, urban roads are multi-lane, and the distance between adjacent lanes in China is 3.75 m. It is well known that it is hard to acquire good performance only with the barrier itself when the source is located away from the barrier. In order to improve the noise reduction effect through active noise control methods, it is necessary to investigate the effect of the additional source on the sound field when the primary source is located away from the barrier. Therefore, the directivity of the sound field at the top of the barrier is calculated in this section, when the primary source is located away from the barrier, as well as when multiple sources exist. The calculation scheme is the same as mentioned above. In the calculation process, the primary source is located at (0.75 m, 0.5 m), 5.75 m away from the center of the barrier. The calculation results are shown in Figure 5, when the additional source is located at 0.3 m, 0.5 m, and 1 m. It can be seen from Figure 5 that the calculation results are similar to those shown in Figure 3. At the frequency of 500 Hz, the SPLs are the smallest when the additional source is located at 0.5 m above the ground, and in the frequency range over 500 Hz, the SPLs are the smallest when the additional source is located at 0.3 m above the ground. It can also be seen that the effect of the additional source location is small in the frequency range over 800 Hz. Therefore, the distance between the primary source and the barrier has little effect on the arrangement of the additional source.