**3. Passive noise control along the propagation path**

The intensity of a sound wave is the acoustic energy carried by the wave per unit of area and per unit of time. It can be computed as the relation between the squared sound pressure and the acoustic impedance of the propagation medium. Thus, two possible ways to reduce the sound intensity are acting directly on the sound pressure or acting on the acoustic impedance along the propagation path.

#### **3.1 Changes in acoustic impedance along noise path**

A change in the acoustic impedance *Z* along the sound path imposes a modification on the sound wave amplitude. When a sound wave intends to pass from a propagation medium **1** with acoustic impedance *Z1* to another medium **2** with acoustic impedance

*Z2*, the fraction of its intensity transmitted from **1** to **2** is determined by the transmission factor *Ft*. The non-transmitted energy goes back to medium **1**, according to the reflection factor *Fr*. These factors can be written as relations between *Z1* and *Z2* [6]:

$$F\_t = \frac{4\ Z\_1 \mathcal{Z}\_2}{\left(\mathcal{Z}\_1 + \mathcal{Z}\_2\right)^2}; F\_r = \left(\frac{\mathcal{Z}\_1 - \mathcal{Z}\_2}{\mathcal{Z}\_1 + \mathcal{Z}\_2}\right)^2 \text{with } F\_t + F\_r = \mathcal{I} \tag{2}$$

If *Z1* and *Z2* have close values, *Fr* will approach to zero and most of the acoustic energy will be transmitted. If *Z1* and *Z2* are very different, most of the acoustic energy will be reflected. Generalizing, a large difference between the impedances of the two media reduces the transmitted acoustic energy. Then, when passing from **1** to **2**, most of the acoustic energy will not be transmitted and the same will occur when passing back from **2** to **1**. This principle is used for the design of composite materials for acoustic insulation, but it is also suitable for controlling solid-induced noise and vibrations. In the first case, the best materials for acoustic insulation of airborne noise are those with very high acoustic impedance, because the acoustic impedance of the air has a low value (around 415 rayl).

When vibrations and/or solid-induced noise are to be controlled, one of the preferred solutions is "cutting" the propagation path and filling the joint with a soft material whose acoustic impedance value is as far as possible from that of the transmission medium. It is a common solution when building double walls to have independent foundations, but also the principle of floating floors and a good option for damping/insulating floor- or wall-transmitted vibrations.

**Table 4** presents the value of longitudinal sound velocity, density, and acoustic impedance for some materials, including some types of common polymers.

#### **3.2 Acoustic barriers or screens**

The main parameter to describe the performance of acoustic barriers is the insertion loss (IL), which represents the difference between the SPL at a receiver without and with the barrier. The maximum value of IL that can be theoretically achieved is 20 dBA for thin screens and 23 dBA for earth embankments [15].

## *3.2.1 How does an acoustic barrier work?*

An acoustic barrier or screen consists of an obstacle—usually, similar to a wall that stands between a sound source and a receiver, and whose characteristics are defined to acoustically protect the receiver. The length of the screen normal to the source-receiver line may be greater than the wavelength for which the barrier is designed. Acoustic barriers aim to create a relatively calm and silent space behind it, in the so-called "acoustic shadow area," even at a short distance from any relevant sound source. The most frequent applications of acoustic barriers are concentrated around highways and railways, in construction sites and mining areas, in the vicinities of airports and industrial zones. They may be placed as close to the source as possible, to maximize their performance. Even though, sometimes it is necessary to put them close to the neighborhoods to protect them against the noise from different sources.

Four types of phenomena occur in an acoustic barrier: reflection, absorption, refraction, and diffraction (**Figure 4**).
