# On the Control of Low-Frequency Audible Noise from Electrical Substations: A Case Study
## 3 Results and Discussion
### Noise Barrier  
A traditional mitigation action is to build a sound barrier with appropriate dimensions, taking into account the safety size and position constraints given by the presence of the HV conductors. [PERSON] computes the intensity diffracted by a barrier, \(I_{\text{diff}}\), with the well-known formula of [PERSON] and [PERSON] [37]  
\[I_{\text{diff}}=I\times\frac{\tanh(\sqrt{2\,\pi\,|N|}}{\sqrt{10}\times\tanh( \sqrt{2\,\pi\,|N|}}\, \tag{9}\]  
where  
\[N=\frac{2\,\delta\,f}{c_{0}}\, \tag{10}\]  
and \(I\) is the direct intensity component without barrier, \(N\) is the Fresnel number, \(\delta\) is the difference between diffracted and direct paths, \(f\) is the frequency and \(c_{0}\) is the speed of sound in air.  
After accurate analysis of the layout, it has been concluded that the maximum height and shortest distance from TR1 and TR2 transformers' cases ensuring safe operations are 5.5 m and 2.1 m, respectively. A new simulation has been performed with a 24 m long barrier that follows these indications. The material chosen for the barrier are commercial concrete blocks featuring resonators [38], whose sound absorption coefficient as a function of frequency is given in Figure 15.  
Figure 14: Comparison between the narrow band sound pressure spectrum and the equal loudness contour intersecting the highest frequency component around 300 Hz.  
Figure 15: Sound absorption coefficient of the bricks chosen for the barrier (from [38]).  
The impulse response computed at the receiver by the simulation software is shown in Figure 16.  
Comparing the normalized impulse response calculated with the barrier, Figure 16, with the one in Figure 13, it can be observed that the first peak is now delayed since the sound must overcome the barrier to reach the receiver. The wall diffracts and scatters part of the early components, creating a broader profile. On the other hand, it redirects the energy intensifying some of the late reflections (peak at 1.3 s). The sound pressure level at the receiver in this case is 32.8 dB(A), 10.1 dB less intense than the sound pressure level without barrier, but the sound component reflected from the buildings located south of the sources towards the receiver can still be reduced by improving the shape of the barrier. Based on these considerations, it is convenient to introduce two lateral baffles with a height of 5 m and a length of 5 m, orthogonal to the main wall as illustrated in Figure 17. The normalized impulse response computed by [PERSON] in this situation is shown in Figure 18. The effect of the lateral diffraction is less evident and the peak at 1.3 s which was visible in Figure 16 is strongly reduced. The sound pressure level computed at the receiver is 28.4 dB(A), 4.4 dB below the value obtained for the simple barrier without extensions, yielding a total reduction of 10.1 + 4.4 = 14.5 dB in comparison with the situation without barrier.  
Figure 16: Impulse response at the receiver with a 24 m long, 5.5 m high straight barrier placed 2.1 m far from the transformers.  
Figure 17: Predicted overall A-weighted SPL distribution in the investigated area, 4 m above the ground, after the installation of the baffled barrier.  
Figure 17 shows the sound pressure level distribution at a height of 1.7 m from the ground. From a comparison between Figure 10 and Figure 17, the mitigation effect of the barrier on the SPL distribution is evident. The addition of more barrier elements south of the sources could further reduce the noise disturbance, but this would create some problems in terms of visibility (the equipment must be \"visible for observation\" [13]) and maintenance (the south edge is the only one free from obstacles with the proposed solution, thus it would represent the preferred access way for operations on the transformers).