*3.2.4 Minimum length of a noise barrier*

To calculate the minimum length of a barrier, the most important variable is the angle of view of the receiver (**Figure 6**). If the angles of view of the receiver are *α* and *β*, the acoustic energy that can reach it will be proportional to the ratio between (*α* + *β*) and the straight angle of which they are part. Thus, if the receiver is located at a distance *d* from the road, the expected sound pressure level at its location will be [18]:

$$L\_{p,d} = L\_d - IL + 10\log\frac{180^\circ - (a+\beta)}{180^\circ} \tag{7}$$

where *Lp,d* is the SPL at distance *d* from the source, with the screen; *Ld* is the SPL at the same point, without the screen; IL insertion loss of the noise barrier, if infinite; and *α*, *β* are the angles of direct view of the source from the receiver, at both sides of the screen.

The relation between the IL and the shielding angle from the receiver does not depend on the distance from the receiver to the barrier, as stated by Ross et al. [27] after analyzing a set of 300 sites with barriers from 90 to 1100 m in length. When studying the behavior of barriers of the same length and different heights, the shielding angle should be at least 165° to reach a good IL value. The effectiveness of the barrier will have an abrupt depletion if the shielding angle is less than 140°. These results backup the usual recommendation of having a shielding angle of at least 160°, which is rather the same as having a barrier length of at least four times the distance *d* on each side of the receiver to be protected. (Strictly, the value should be closer to / between 6–7.5*d*).

#### *3.2.5 Headers or cappings*

While the basic design of a noise barrier involves defining the location, height, and materials of a wall with a horizontal top edge, there are many possible designs for capping the wall. Headers or cappings are very important in the acoustic performance of barriers. Although they also have an esthetic function, headers seek to improve

**Figure 6.** *Sketch for calculating the length of an acoustic screen (adapted from Ref. [18]).*

noise reduction achieved by diffraction at the upper edge of the screen. There are cantilevered cappings, multi-diffraction, tubular, Y-shaped, absorptive or reflective ones, designs for promoting destructive interference, sound diffusion or scattering. There are even patented acoustic header designs for acoustic barriers. A broad catalog of tested header designs can be found in Ref. [26]. The excess attenuation is near 2 dB, but an extra attenuation of up to 6 dB can be achieved. When comparing the performance of two thin barriers of the same height in the same construction site, one of them having a straight edge cantilever and the other one, a slanted flat-tip jagged cantilever, the last one achieved an additional attenuation of up to 5 dBA [28]. Last but not least, there are many designs of cappings that includes ANC technologies.
