2. QRD (quadratic residue diffusers)

The surface pattern of these diffusers can be one or two dimensional. The first ones have linear openings of the same width and different depths. The depths are obtained by a periodic sequence. The two-dimensional QRD have square cavities of different depths.

### 3.PRD (primitive root diffusers)

They have linear openings of different depths, but they do not suit a periodic pattern because of the number sequence used for the design.

## 4.2 Crystal-structured diffusers

A crystal structure is an atomic or molecular basic pattern that is identically repeated for many times with the same special distribution and the same

performance of a wall. Two of the main causes of this are the presence of weak points or cavities and the contributions by nondirect transmission (lateral and/or

Weaknesses and weak points are usually related to cracks in doors and windows, poor sealed joints, passes for electric and sanitary channeling, construction defects, and interstices. The greater the area of the imperfections, the more they will weaken

Side or flank transmissions can be as or more important than direct transmission through a wall. They can lead to a significant decrease in the expected insulation. Sound transmission by flanks occurs when the lateral divisors are considerably lighter and/or rigid than the main wall. To solve these issues, the acoustic

quality of the laterals needs to be improved to avoiding a poor performance of the

solid), which are usually not considered in the calculations.

Acoustic insulation of some tested double walls (values from [8–10]).

Description m(kg/m<sup>2</sup>

15 cm brick wall with plaster, plus 25 mm glass wool plus 4 cm air chamber plus 25 mm glass wool plus 7

30 cm brick wall plus 50 mm glass wool plus 12 cm air chamber plus 30 cm bricks with plaster

Two 6 mm plywood panels, each one glued to both faces of wood crossbars of 2.5 cm x 7.5 cm and 41

Two 6 mm plywood panels, each one glued to both faces of wood crossbars of 2.5 cm x 7.5 cm and 41

Two 5 mm plywood panels with 1.5 mm lead foil

7 cm light concrete plus 1.5 cm plaster, 20 mm glass wool, 3 cm air chamber, 5 cm light concrete plus 1.5

20 cm concrete plus 25 mm glass wool plus 12 cm air chamber plus 25 mm glass wool plus 15 cm brick

9 cm concrete plus 2.5 cm air chamber plus 65 mm rigid glass wool panel plus 9 cm concrete plus 16

9 cm concrete plus 6 cm air chamber plus 65 mm rigid glass wool panel plus 9 cm concrete plus 16

Two 12 mm gypsum plates with a 7 cm air chamber

One gypsum plate 2 x 12 mm and one 12 mm gypsum plate with 7 cm air chamber between them

Two 2 x 12 mm gypsum plates with a 7 cm air

and 50 mm glass wool between them

Two 12 mm gypsum plates with a 2 cm air chamber

cm separation plus 10 cm air chamber

cm concrete

Acoustics of Materials

cm separation

between them

cm plaster

mm gypsum plate

mm gypsum plate

chamber between them

between them

wall

) Frequencies (Hz)

350 40 54 57 65 70 76

s/d 80 90 98 109 111 111

12.2 16 18 26 28 37 33

14.1 14 20 28 33 40 50

25 26 30 34 38 42 44

450 24 33 41 50 60 65

650 63 72 74 85 91 93

s/d 49 54 57 56 71 81

s/d 57 65 76 82 86 83

s/d 13 21 33 43 44 39

s/d 18 25 39 47 49 44

s/d 23 30 45 49 52 52

s/d 21 35 48 55 56 43

125 250 500 1000 2000 4000

the acoustic insulation of the wall.

solution.

16

Table 2.

orientation. The attraction forces are maxima and are responsible for maintaining the crystal structure.

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A sound crystal is also a repetitive structure that causes a recursive scattering by diffraction one time and another [11]. The repetitive properties are the density and the sound propagation speed of the materials that compose the crystal. To meet the desired effect, the wavelength to be controlled should be similar to the dimension of the materials. Crystal sound diffusers have different applications; for example, they are used for the top part of sound barriers.
