**2. Background**

Acoustic barriers have been widely used when noise control on the propagation path is needed, once there are no other possibilities of control on the source [2]. Up to five acoustic phenomena can occur in an acoustic barrier: sound reflection, transmission, absorption, diffraction, and scattering.

The material of the surface exposed to the source is what defines the amount of acoustic energy that will be scattered, absorbed, and reflected. When there are barriers on both sides of a source and their surface materials are not adequate for sound absorption, sound pressure levels may increase due to multiple reflections between the two sheets of the acoustic barrier [3]. The acoustic impedance of the material of the barrier determines the amount of acoustic energy that will be transmitted through it. It is generally assumed that if a material has a surface density of at least 10 kg/m<sup>2</sup> (kilogram per square meter), it is suitable for acting as a noise barrier [2].

Finally, diffraction should be the predominant acoustic phenomenon in a barrier. It refers to the fact that sound waves change direction, edging the obstacles they find in their path, which, in the case of a barrier, occurs at the top edge but also at the side edges [2].

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

The attenuation provided by an acoustic barrier is called *insertion loss* (IL), which is defined as the difference between the direct sound pressure level obtained in the absence of an acoustic barrier (Ldir), and the level obtained with the presence of the barrier, i.e., the diffracted sound pressure level (Ldif) [2] (see Eq. (1)).

$$\text{IL} = \text{L}\_{\text{dir}} - \text{L}\_{\text{dif}} \tag{1}$$

The proposal of Maekawa to calculate the IL value from the Fresnel number N marked a milestone in the development of noise barrier research (Eq. 2). A detailed analysis of Maekawa's work can be found in [4].

$$\text{IL} = \text{10 } \log \ (20 \text{ N}) \tag{2}$$

where *<sup>N</sup>* <sup>¼</sup> <sup>2</sup> *<sup>δ</sup> <sup>λ</sup>* is the Fresnel number

λ = the wavelength of sound (in meters) at the considered frequency *f*, and.

δ = *a+b – d* is the difference between diffracted sound path and direct sound path (in meters) (see **Figure 1**).

Since Maekawa's first approach had some limitations, some authors have worked on finding a better calculation method to predict the IL of acoustic barriers [2]. In next sections, some of them will be presented.

### **2.1 Thick barrier approach**

An acoustic barrier is said to be "thick" when it has more than one point where diffraction can occur [2].

A barrier is considered thick when:


Eq. (3) can be used for solid barriers either thin or thick. In the case of thick barriers, the thickness *t* is added to the smallest of the distances *a* or *b* and with this

**Figure 1.** *Cross section of an acoustic barrier (adapted from [2]).* new value *a'* or *b'*, the Fresnel number N should be calculated. Then, the insertion loss will be obtained through Eq. (3) [2].

$$\text{IL} = \text{10 } \log \left( \text{3} + \text{10 } \text{N} \cdot \text{K} \right) - \text{A}\_{\text{gr}} \tag{3}$$

Where:

N: Fresnel number calculated by considering the hypothesis of thick barrier, Eq. (4) (see **Figure 2**):

$$N = \frac{2}{\lambda}(a' + b - d) \tag{4}$$

For a thick barrier, the value of *t* must be added to the minimum of *a* and *b*; the values corrected this way are noted as *a'* or *b'*.

K: meteorological correction, with.

K = 1 for distances between source and receiver either less than 100 m or greater than 300 m.

Otherwise:

$$K = e^{-0.0005\sqrt{\text{abd}/N\text{à}}}$$

Agr: ground attenuation along the sound path.

The barrier attenuation should not be assumed to be greater than 20 dB.

### **2.2 Kurze-Anderson approach**

This way of obtaining IL is a general one. The expressions to be used are those of Eq. (5) [2].

$$\text{If N} > 12.5 \qquad IL = 24$$

$$\text{If } -0.2 < \text{N} < 12.5 \, IL = 5 + 20 \, \log \frac{\sqrt{2\pi N}}{\tanh \sqrt{2\pi N}} \tag{5}$$

Where N is the Fresnel number defined in Eq. (4)

$$\text{Remember that } \tanh X = \frac{\sinh X}{\cosh X} = \frac{e^X - e^{-X}}{e^X + e^{-X}}$$

**Figure 2.** *Cross section of a thick barrier (adapted from [2]).*

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

### **2.3 Green barriers**

The case of tree or green barriers is rather different. Just as in "conventional" barriers, the hermeticity of the material is central, it is necessary to assume that the tree barriers are non-soundproof. In turn, scattering may homogenize the acoustic field into the tree plantation. On the other hand, among the characteristics of the vegetation that participate in the attenuation of the barrier, the density of the plantation, distance between trees, geometric pattern of the plantation, the features of trunks, bark, and canopy, and the dimensions of the leaves, whether the trees are deciduous or evergreen. The abovementioned points are presented in Section 2.3.1.

One simple point for expecting a good sound attenuation performance in a tree barrier is that it must block the visuals between source and receiver, as stated by ISO 9613-2 [5]. If the receiver is able to be seen from the source and through the vegetation, it is most probable that the barrier will not be dense enough for sound attenuation.

## *2.3.1 An overview of the research on green barriers*

The acoustic of forests began to be studied in 1946 by Eyring [6], who found an attenuation of 0.05–0.13 dB/m (decibels per meter), increasing with frequency. Some years later, Embleton [7] and Aylor [8, 9] continued with Eyring's work. Embleton [7] obtained an important depletion of 7 dB/100 ft. (decibels each 100 feet) for frequencies below 2000 Hz. He tried to explain such high results thinking about branches as resonance absorbers, but his theory was not easy to be proven. Recent works, as Johansson's [10], show that the forest is a complex system that can reduce (absorb) or amplify sound pressure levels, depending on the phenomena that are activated for each case.

Aylor [8] showed that plants have a good behavior for noise control. He worked with pink noise attenuation through a dense reed marsh (*Phragmites communis*). The average height of the reeds was 2.5 m, the area of leaves per volume unit of canopy was 3.0 m<sup>2</sup> /m<sup>3</sup> , and the density of plants was 59 10 plants/m<sup>2</sup> . The average width of the leaves was 3.2 cm. Aylor found an increasing attenuation between 500 Hz and 10,000 Hz, with an increasing rate close to 4–4.5 dB/octave. He found an attenuation close to 18 dB at 10,000 Hz for 12.2 m broad of reeds. When comparing with corn plants (*Zea mays*) attenuation, he found that the best performance was at a frequency of 2000 Hz; the width of the corn plants leaves was 7.4 cm in average. In another study, Aylor [9] measured the sound attenuation related to trunks and stems. He used field corn (*Z. mays*), hemlock (*Tsuga canadensis*), red pine (*Pinus resinosa*), and a hardwood brush of about 6 m in height. He found the denser the plantation and the greater the leaves surface, the better the attenuation. Also, the trunks have an important effect on sound scattering, whether the wavelength was small in comparison to the radius of the trunk.

Price et al. [11] measured and studied different forests sound attenuation: Norway spruce (*Picea abies*) and oaks, with a dense undergrowth; a monoculture of Norway spruce of 11–13 m in height; a coniferous plantation including red cedar (*Thuja plicata*), Norway spruce, and Corsican pine (*Pinus nigra*). Summer and Winter measurements were performed. A general attenuation pattern was found, with a first absorption peak at about 250 Hz; a region of poor absorption performance and possible resonant amplifying, around 1000–2000 Hz; and a second attenuating region, from 2000 Hz to 10,000 Hz approximately. The authors aimed to build a predictive model, by adding the contributions to sound attenuation of ground, trunks, and

foliage, calculating each one separately. On the other hand, Lee et al. [12] examined 15 sites with coniferous trees, along some roads in Virginia, USA. They concluded that only a very poor sound attenuation could be attributed to the trees. They found no differences according to the trees age, height, species, nor density at the sites.

Huddart [13] stated that noise barriers such as walls, fences, or mounds of earth are often used to reduce noise pollution from traffic, but that a tree belt would be a more environmentally friendly and esthetic option. He measured the attenuation of traffic noise through five types of vegetation up to a depth of 30 m. He verified that the foliage is important in reducing the high frequencies (above 2000 Hz), while the middle frequencies (250–500 Hz) are attenuated by the absorbent qualities of the ground. The ground absorption features can be enhanced by the roots of the plants and litter.

Huisman and Attenborough [14] showed that the acoustic response of a forest directly depends on the type of wave interference: for constructive interferences (coherent waves), sound reverberation is expected; otherwise, attenuation of the sound may occur. The authors stated that sound scattering by atmospheric turbulence is a well-known phenomenon, related with loss of coherence of waves, for wavelengths minor than the trunk diameter.

Alessandro, Barbera and Silvestrini (1987) and Stryjenski (1970), cited by Ochoa de la Torre (1999) [15], proved that the acoustic absorption of some plant species varies with the size of the leaves and the density of the foliage. Thus, noise levels decrease should only be expected for frequencies above 2000 Hz, with attenuation values of 1 dB every 10 m of depth, up to a maximum of 10 dB at 100 m or more. Furthermore, Ochoa de la Torre (1999) cites Cook and Haerbeke (1971) and Alessandro et al. (1987) that, among other conclusions, stated that: "*a screen placed close to the source is more efficient than another next to the area to be protected*"; and that "*the species to be used must be evergreen, avoiding conifers, which are the least efficient.*"

In the same direction, Tarrero (2002) [16] cites Martens and Huisman (1986), who showed that deciduous trees attenuate more than grass without trees but less than evergreen ones.

In 2002, Tunick [17] linked meteorology and sound propagation in a forest. He found a microclimate, where temperature and wind velocity are rather uniform. The main attenuation phenomena in the forest are: interfering between sound waves, both direct and reflected on the ground; scattering and absorption by ground, trunks, branches, and atmospheric turbulence. In the range of medium frequencies (250– 500 Hz), ground impedance is one of the most influencing factors. For frequencies from 1000 Hz to 2000 Hz, the trunks, branches, and canopy are the main agents, acting both by sound scattering and sound absorption. For these high frequencies, these phenomena seem to have more incidence on sound attenuation than refraction effects related to the microclimate in the forest.

Martínez Sala et al. [18] carried out a study with vegetable plantations (poplars, cypresses, laurels, and orange trees), demonstrating that it is possible to improve the sound attenuation obtained from a mass of trees if their elements are ordered in a periodic way. They worked with an arrangement in regular rows, a square, rectangular, and triangular configuration of the trees. Their experimental results showed that the highest sound attenuation was obtained for a range of frequencies related to the periodicity of the array. This behavior led them to intend that these sets of trees can be seen as sonic crystals. The experimental results showed that a belt of trees organized in a periodic matrix produces attenuation peaks at low frequencies (f < 500 Hz), not as a consequence of the ground effect but as a result of the destructive interference of scattered waves. Therefore, these periodic arrays could be used as plant acoustic screens. *Evaluation of Industrial Noise Reduction Achieved with a Green Barrier: Case Study DOI: http://dx.doi.org/10.5772/intechopen.108835*

Onuu [19] found that grass can introduce an attenuation in all frequencies twice the amount of attenuation of a forest. The best performance was measured between 1000 Hz and 4000 Hz. He also stated that the best relation for representing the attenuation of grass is logarithmic, whether for trees is a power equation.

Swearingen and White [20] proposed an adjustment of the calculation method of Defrance, to include other atmospheric phenomena, especially those related to scattering. As that previous model did, they used the Green's function parabolic equation (GFPE) for modeling different phenomena that they also measured. The authors added those phenomena one by one to their simulation, and they found that the atmospheric condition had strong influence on sound propagation. Trunks and canopy scattering became more important at greater distances to the source, but they had not a significant influence on sound pressure levels, when compared to the atmospheric incidence.

In their exhaustive analysis of noise barriers, Kotzen and English [3] state that the best performance of a green barrier occurs at a frequency for which the wavelength is twice the size of the leaves of the trees or shrubs. It makes sense with Aylor's findings [8, 9], more than 30 years earlier. According to [3], green barriers are not expected to control sounds of frequencies lower than 250 Hz, and their best performance is for frequencies of 1000 Hz and higher.

Fan et al. [21] did many measurements behind six dense hedges involving six different evergreen species: arrowwood (*Vibumum odoratissimum*), oleander (*Nerium indicum*), Chinese Photinia (*Photinia serrulata*), bamboo (*Oligostachyum lubricum*), Red Robin Photinia (*Photinia fraseri*), and Deodar Cedar (*Cedrus deodara*). The authors found the best performances for the so-called "leaf shape" (the relation between leaf length to leaf width) between 2 and 3, for the greater leaf area and leaf weight: between 3 and 4 dB/m. Bamboo and oleander did not exhibit good attenuation, but deodar cedar presented very good attenuation at low frequencies (lower than 100 Hz and between 250 Hz and 800 Hz). On the other hand, both *Photinia* species and arrowwood showed their greatest attenuation at frequencies higher than 2000 Hz. Thus, the authors recommend using different kind of species in order to enhance the acoustic behavior of a hedge. They obtained Eq. (6) by regression, and they propose it for calculating the sound attenuation of hedges, in dB/m.

$$
\Delta \text{L}\_{\text{Aep}} \,\text{(dB/m)} = 2.705 + 0.266 \,\text{W} - 3.337 \,\text{T} - 0.094 \,\text{S} \tag{6}
$$

Where:

W is the leaf weight (g)

T is the tactility; T = leaf weight/leaf area (g/cm2 )

S is leaf shape; S = leaf length/leaf width (m/m)

Horoshenkov et al. [22] demonstrated the importance of the characteristics of leaves for their acoustic performance, especially as sound absorbers. The authors worked with five kinds of plants (*Geranium zonale, Hedera helix, Pieris japonica, Summer Primula vulgaris,* and *Winter P. vulgaris*). The laboratory work was done using an impedance tube (or Kundt tube). The authors also measured the thickness, weight, and area of single leaves, the number of leaves on a plant, the volume occupied by the plant, the dominant angle of leaf orientation, the total area of leaves by plant, the surface density of a single leaf, and the total weight of leaves and stems. The *Winter Primula Vulgaris* had the best acoustic performance, with an absorption coefficient of 0.6 or greater for frequencies between 500 Hz and 1600 Hz. The lowest absorption coefficient was that of *H. helix*, with values lower than 0.2 for all frequencies lower than 1600 Hz.

According to Asdrubali et al. [23], the most important part of the attenuation in a forest is provided by the ground surface. They stated: "*the main absorber is the substrate soil ( … ). The presence of the plants becomes useful only when a large number of them is installed on the sample, otherwise is even pejorative within some frequency ranges.*"

On the other hand, contemporaneously, Azkorra et al. [24] obtained a weighted sound absorption coefficient of 0.40 with the best absorption behavior at frequencies of 125 and 4000 Hz, and the worst ones at 500 and 1000 Hz.

Li et al. [25] demonstrated that most of the sound absorption by trees is due to its bark properties. The rougher the surface of the bark, better sound absorption performance would be expected. When the bark had moss, the acoustic performance was significantly enhanced. In any case, the absorption coefficients for normal incidence in the range of 160–1600 Hz are actually low: the highest measured values were about 0.1, broadleaved trees having worse results than coniferous trees.

## *2.3.2 Hoover's expression*

According to Palazzuoli and Licitra [26], the attenuation of noise traveling a distance *df* through a dense forest can be estimated using Hoover's expression (Eq. (7)).

$$A\_f = \frac{d\_f}{100} f^\ddagger \tag{7}$$

Where *df* is the distance through the forest, in meters *f* is the frequency, in Hz

### *2.3.3 ISO 9613-2 approach*

The broadly used ISO 9613-2 Standard [5] also considers the attenuation of green barriers as one of the sound attenuation terms, such as geometric divergence Adiv, atmospheric absorption Aatm, ground attenuation Agr, presence of obstacles Abar, and miscellaneous attenuation Amis. One of the miscellaneous attenuation phenomena is just the propagation through foliage Afol. The general equation is Eq. (8).

$$\mathbf{A} = \mathbf{A}\_{\text{div}} + \mathbf{A}\_{\text{atm}} + \mathbf{A}\_{\text{gr}} + \mathbf{A}\_{\text{bar}} + \mathbf{A}\_{\text{mis}} \tag{8}$$

The main terms for obtaining the sound attenuation, Adiv, Aatm, and Agr, are presented below. In turn, Afol is also presented.
