## 3 Numerical Results
### Acoustical Analysis
The AoA variation of the interpolation control in Figure 8d is reduced about 1\({}^{\circ}\). According to the rule of a 1\({}^{\circ}\) AoA reduction resulting in a 1 dB noise reduction [39], the noise change in the present study is within this range. For comparison, it can be observed that the differences between the controlled and uncontrolled results of A-weighted SPL regarding all the cases are negligible. The reason is that the  
Figure 12: Sound pressure level in function of blade azimuth angle without control at 1.5 m height and 500 m distance downstream from the turbine at a wind speed of 6 m/s. A-weighted SPL accounts for more of the high-frequency noise to which humans are more sensitive and de-emphasizes the low-frequency contribution. In our case, the reduction of the noise mainly occurs in the low-frequency part and thus the A-weighting SPL is similar in all the cases. It should be noted that the low-frequency noise is important in far-field as it can propagate in a long distance with very small air absorption. To check the AM noise, the modulation depth for Case 4 is calculated according to the method proposed in [7] and shown in Table 3. From the table, it is seen that the modulation depth is slightly reduced. Figure 13: Sound pressure level and A-weighted sound pressure level of the turbine at 6 m/s wind speed: (**a**) sound pressure level (SPL) for Case 1; (**b**) A-weighted SPL for Case 1; (**c**) SPL for Case 2; (**d**) A-weighted SPL for Case 2; (**e**) SPL for Case 3; (**f**) A-weighted SPL for Case 3; (**g**) SPL for Case 4; (**h**) A-weighted SPL for Case 4. Moreover, this phenomenon can be verified in Figure 14, where the contribution of SPL in different frequencies at the time instant (120 s) is shown. From the figure, it is seen that at the low frequency (which is less than 315 Hz), SPL is reduced obviously by the pitch control strategy. Figure 15 illustrates the SPL and A-weighted SPL in Cases 1, 2 and 4, but with a lager inflow wind speed of 10 m/s. With the lager wind speed, the SPL increases about 8.5 dB in each case. The interesting thing observed to be noticed is that the pitch control methods at 10 m/s display a similar effect in Case 4 as at 6 m/s but the variations in amplitude are more important. Since the A-weighted SPL was designed according to human hearing and emphasizes the contribution from the high frequency sound centered at 1000 Hz, it can give an impression that the control methods give a small effect on A-weighted SPL. The modulation depth is listed in Table 3 and a small reduction is seen. It is worth noting that the yaw and shear considered in this study are relatively small and these effects can be much bigger in large shear and yaw cases. Moreover, the noise propagation effects due to changing atmospheres and wakes [8] are not included here. In the future, the present noise source-modelling framework will be further coupled with the propagation model [8] in order to control wind turbine noise at far field. \begin{table}
\begin{tabular}{c c c c} \hline condition & 6 m/s no control & 6 m/s full control & 6 m/s inter control \\ modulation depth (dB) & 0.3331 & 0.3127 & 0.2736 \\ condition & 10 m/s no control & 10 m/s full control & 10 m/s inter control \\ modulation depth (dB) & 0.4308 & 0.3834 & 0.3692 \\ \hline \end{tabular}
\end{table} 
Table 3: Modulation depth for Case 4. Figure 14: SPL spectra of case 4 of the turbine at 6 m/s wind speed at a time instant of 120 s after control.