## 3 Experiment Results  
### Effect of the Aspect Ratio  
The far-field _SPL_ and _dSPL_ of different cylinders at the #1 microphone (U = 30 m/s) are shown in Figure 6. The _dSPL_ is the increment in the sound pressure level between the wavy cylinders and the baseline cylinder (#0 cylinder). Obviously, the #0 cylinder has the largest far-field _SPL_ among all the cylinders at the #1 microphone position when U is 30 m/s. All the wavy cylinders have an obvious reduction in the far-field _SPL_, and the noise reduction effect is similar. Specifically, the #2 cylinder has the best performance for noise reduction, whose aspect ratio is 30. If the aspect ratio is decreased from 30 to 24, the far-field _dSPL_ is decreased instead of increasing. The variation of the far-field _dSPL_ is not monotonous. Further analysis showed that there are several single troughs of far-field _dSPL_ between 200 Hz and 1000 Hz. Therein, the largest one exceeds 37 dB occurring between 200 Hz and 300 Hz when \(\lambda/a=30\). The far-field _dSPL_ has a slight increasing when \(\lambda/a=40\). The frequency occurring the largest far-field _dSPL_ for all the wavy cylinders is very close, which is between 200 Hz and 300 Hz. Figure 7 gives the far-field _SPL_ and _dSPL_ of the #2 cylinder at different microphone locations (U = 30 m/s). The far-field _dSPL_ is the increment of _SPL_ between the #2 cylinder and #0 cylinder at the same microphone location. At different locations of the microphone, the far-field _SPL_ of the #2 cylinder is very close beyond the frequency of 200 Hz when U = 30 m/s. Moreover, the far-field _dSPL_ is also very close within all the frequencies. Meanwhile, several single troughs of far-field _dSPL_ appear within the frequency between 200 Hz and 1000 Hz. Finally, the largest one also occurs between 200 Hz and 300 Hz. Figure 6: Far-field _SPL_ and _dSPL_ of different cylinders at #1 microphone (U = 30 m/s). The _OASPL_ of different cylinders (U = 30, 40, 50, 60 m/s) is presented in Figure 8. The _OASPL_ is integrated within the specified frequency range (as shown by Formula (6)). Compared with the baseline cylinder (the #0 cylinder), all the _OASPL_ distributions for the wavy cylinders in the polar curve show a significant reduction trend at the position of each microphone. In addition, there is just a slight difference in _OASPL_ among the #1, #2 and #3 cylinders with a large spanwise wavelength and a large aspect ratio. Therein, the _OASPL_ reduction of the #2 cylinder is the largest, followed by the #3 cylinder and the #1 cylinder. Figure 8: _OASPL_ of different cylinders (U = 30, 40, 50, and 60 m/s). Figure 7: Far-field _SPL_ and _dSPL_ of the #2 cylinder at different microphone locations (U = 30 m/s). Figure 9 presents the _DOASPL_ between the baseline cylinder and the wavy cylinders with different aspect ratios (U = 30, 40, 50, and 60 m/s). The _DOASPL_ is the increment in _OASPL_ between the baseline cylinder (the #0 cylinder) and the wavy cylinders within the specified frequency range (as shown in Formulas (6) and (7)). Obviously, all the wavy cylinders with a large aspect ratio and large spanwise wavelength have a large noise reduction effect. The minimum _DOASPL_ is 13.6 dB, and the maximum is 20.08 dB; the average is more than 16 dB. The noise reduction of the #2 wavy cylinder (\(r\) = 30) is the largest, but it decreased slightly when \(r\) = 40 and \(r\) = 24. Further observation shows that upstream noise reduction is more obvious than that downstream. The averaged _DOASPL_ between the baseline cylinder and the wavy cylinders with different aspect ratio (U = 30, 40, 50, 60 m/s) is shown in Figure 10. The aspect ratio (r) divided by the averaged _DOASPL_ is linear with the 2 power of aspect ratio (r), as shown in Formula (8). The difference in the slope of the curves is very small under different airflow speed, wherein the slope when U = 50 m/s is the lowest.