**5. Acoustic performance of the green barrier**

## **5.1 Finding the depletion law of the noise source**

The source's emission spectrum measured at 12 m was propagated to obtain the expected spectrum at P2, considering Adiv and Aatm. For calculating Adiv, both spherical and cylindrical propagations were tested, i.e., applying Eqs. (9) and (12), respectively [1].

$$L\_{p,r\_1} = L\_{p,r\_0} - 10\ \log\left(\frac{r\_1}{r\_0}\right) \tag{12}$$

Where

*r0:* distance from the source where emission sound pressure levels were measured (12 m)

*r1*: distance from the source to P2 (239 m)

*Lp,r0*: measured sound pressure level, at a distance r0 from the source (see **Table 1**) *Lp,r1*: expected sound pressure level, at a distance r1 (in this case, at P2)

Since the distance from the source to P2 is further than 100 m, the atmospheric absorption will also be considered for this comparison. The atmospheric absorption refers to the attenuation of sound due to traveling along a distance *d*. According to [5], it should be calculated by applying Eq. (10).

In this case, the average temperature and humidity conditions at P2 during the sound pressure level measurements (**Table 5**) were T = 25°C and RH = 50%. The values of α in **Table 7** were taken from Miyara [28].

The results are shown in **Table 8** and **Figure 8**. As it can be seen in **Figure 8**, the linear approach fits better the measured values up to 500 Hz. Thus, the calculation method was not that of ISO 9613-2 [5] because the divergence calculation law was assumed to be not quadratic but linear. All the other attenuation terms were calculated according to ISO 9613-2.

#### **5.2 Sound pressure levels at P1, excluding the tree barrier acoustic performance**

813 m. **f (Hz) 63 125 250 500 1000 2000 4000 8000**

SPL at P1 were calculated by using Eq. (12). In this case, r0 was 12 m and r1 was


**Table 7.**

*Atmospheric absorption coefficients by octave bands for T = 25°C and HR = 50% (from [28]).*


#### **Table 8.**

*Comparison of sound pressure levels at P2 using two different depletion laws (all values are in dB).*

*Evaluation of Industrial Noise Reduction Achieved with a Green Barrier: Case Study DOI: http://dx.doi.org/10.5772/intechopen.108835*

#### **Figure 8.**

*Comparison of spectra obtained with linear and quadratic depletion laws and the measured spectrum.*

Atmospheric and ground absorptions were also considered. Since the ground slope between the coal processing mill and Point P1 is rather uniform (**Figure 9**), the calculation approach proposed by ISO 9613-2 [5] for Agr can be used.

The SPL at P1 were measured when the coal mill was the only noise source operating in the plant. Meteorological conditions during the measurements were considered in selecting atmospheric absorption coefficients (T = 20°C and RH = 80%) (see **Table 9**).

The sound path between the mill and P1 consists of various types of soil, as sketched in **Figure 10**. The length and type of surface of each one are summarized in **Table 10**. The detailed method for calculating G can be found at [5].

Taking into account the height of the source hs = 3.6 m and the height of the receiver in P1 hr = 1.5 m, the values of G for each region in **Figure 3** are presented in **Table 11**.

#### **Figure 9.**

*Diagram of the terrain profile from the coal processing mill to P1 (obtained from Google Earth).*


**Table 9.**

*Atmospheric absorption coefficients by octave bands for T = 20°C and HR = 80% (from [28]).*

#### **Figure 10.**

*Diagram of the case study (not in scale).*


### **Table 10.**

*Ground absorption characteristics.*


#### **Table 11.**

*G values and ground coverage, by region.*

The propagation from the sound source, only considering attenuation by distance, by atmospheric absorption, and by absorption from the ground, leads to the results in **Table 12** (calculations were done according to [5]). The 31.5 Hz band was not used, because the atmospheric absorption coefficient does not calculate the same way as it does in higher frequencies.

When comparing the results in the first and the last row in **Table 12**, it appears that the measured values are lower than the ones previously calculated, when expressed in A-weighting scale. The difference is greater at the lowest frequency band and at 1000 Hz and 2000 Hz bands.

According to the background discussed in Section 2, these differences reinforce the hypothesis of an extra sound attenuation, possibly provided by the tree barrier.

*Evaluation of Industrial Noise Reduction Achieved with a Green Barrier: Case Study DOI: http://dx.doi.org/10.5772/intechopen.108835*


#### **Table 12.**

*Expected results for direct propagation, without considering the tree barrier (all values are in dB).*

Tunick [17] states that the trunks, branches, and crowns are the main agents that attenuate sounds from 1000 Hz to 2000 Hz. On the other hand, according to Martínez Sala [18], the attenuation in frequencies lower than 500 Hz is due to the destructive interference of the sound waves when scattered in a belt of trees planted following a periodic pattern.

### **5.3 SPL at P1, considering the tree barrier insertion loss (IL)**

The IL can be calculated using different formulae. Once the direct sound pressure levels Ldir have been calculated considering Adiv, Aatm and Agr (see **Table 12**), the sound pressure levels Ldif can be also obtained by difference, using Eq. (1). It is assumed that the SPL at the receiver were only caused by the sound wave diffracted by the barrier, i.e., no direct sound from the source was expected to arrive to P1. It also must be taken into account that there is diffraction by the lateral edges, which must be calculated and added to the previously calculated SPL at the receiver.

In this case study, IL will be calculated according to different methods, to compare their results. The approaches to be considered are: Kurze-Anderson and thick barrier approach, which are general expressions for solid barriers; and Afol from ISO 9613-2 and Hoover's expression, which are specific approaches for green barriers [1, 2, 5, 26].

#### *5.3.1 Kurze-Anderson approach*

This way of obtaining IL is a general one; it has not been developed for green barriers. It is expected to overestimate the value of IL.

For a thick barrier, the value of *t* (**Figure 2**) must be added to the minimum of *a* and *b*. In this case, since *b* > *a*, then *a'* = *a* + *t*.

Thus, *a* = 278.08 m; *b* = 474.08 m; *t* = 61 m; *a'* = 339.08 m; *d* = 813.00 m.

The IL calculated using Eq. (5) and the SPL expected at the receiver are presented in **Table 13**. Note that the IL for the band of 63 Hz has been considered because the wavelength at this frequency is significantly shorter than the barrier width *t*.

The calculated SPL at 4000 Hz and 8000 Hz were lower than the background noise at P1; thus, they have been replaced by the background values in **Table 2** (figures in green in **Table 13**).
