3. Sound insulation

Airborne sound propagation is usually due to the elastic vibrations of the air due to the sound waves that reach a material surface and excites it. It also occurs, more easily, through evident discontinuities (e.g., openings) or unwanted weak spots (such as cracks, weakly sealed passages for electrical, sanitary or other installations, ventilation ducts, and openings that do not close properly or whose frames are poorly sealed, among other possible imperfections).

#### 3.1 How does sound insulation occur?

The acoustic insulation of a material or a set of them refers to the property to oppose and, consequently, to reduce the flow of acoustic energy that passes through it. A good acoustic insulation reduces the acoustic energy that is received on the other side of it, affecting the amplitude of the wave but not through dissipative phenomena, as the acoustic absorbers do.

The acoustic insulation is based on the modification of the amplitude of a wave when passing from a medium of acoustic impedance Z1 to another of acoustic impedance Z2. The relationship between the acoustic impedances does not only have to do with the modification of the amplitude of the incident wave: it is also related to the fraction of the incident energy that will be reflected or transmitted. Most of the acoustic properties of materials can be studied by the application of new laboratory and numerical methods as ultrasonic characterization [4], inverse characterization with basis on the acoustic impedance measurement [5], or ensemble averaged scattering [6].

The factors of reflection and transmission can be written according to the values of the impedances of the two media involved:

$$F\_r = \left(\frac{Z\_1 - Z\_2}{Z\_1 + Z\_2}\right)^2, \qquad F\_t = \frac{4Z\_1 Z\_2}{\left(Z\_1 + Z\_2\right)^2} \tag{7}$$

It can be seen that for similar values of Z1 and Z2, the reflection coefficient Fr tends to zero, and the more different their values are, the value of Ft tends to zero.

Then, the greater the difference between the values of Z1 and Z2, the greater the fraction of the energy of the incident wave that will be reflected, and, consequently, the non-reflected energy, which comprises the energy absorbed and the energy transmitted, will be lower. Implicitly, even if the absorption were not significant, a large difference between the impedances of the two media tends to reduce the amount of acoustic energy transmitted. Taking into account both premises at the same time, when a wave propagates by air and reaches a material How Do Acoustic Materials Work? DOI: http://dx.doi.org/10.5772/intechopen.82380

As these devices are very selective, they are generally used only when a reverberation has to be eliminated at a well-defined frequency or, in any case, in a fairly narrow frequency range. If some sound absorbent material is placed inside the cavity and especially close to the neck, the range of frequencies absorbed by the resonator can be expanded somewhat, but the efficiency in the frequency of better

The construction of Helmholtz resonators is usually done by panels with circular or linear perforations, where the total area of the resonator is the sum of the areas of

Airborne sound propagation is usually due to the elastic vibrations of the air due to the sound waves that reach a material surface and excites it. It also occurs, more easily, through evident discontinuities (e.g., openings) or unwanted weak spots (such as cracks, weakly sealed passages for electrical, sanitary or other installations, ventilation ducts, and openings that do not close properly or whose frames are

The acoustic insulation of a material or a set of them refers to the property to oppose and, consequently, to reduce the flow of acoustic energy that passes through it. A good acoustic insulation reduces the acoustic energy that is received on the other side of it, affecting the amplitude of the wave but not through dissipative

The acoustic insulation is based on the modification of the amplitude of a wave

The factors of reflection and transmission can be written according to the values

It can be seen that for similar values of Z1 and Z2, the reflection coefficient Fr tends to zero, and the more different their values are, the value of Ft tends to

Then, the greater the difference between the values of Z1 and Z2, the greater the fraction of the energy of the incident wave that will be reflected, and, consequently, the non-reflected energy, which comprises the energy absorbed and the energy transmitted, will be lower. Implicitly, even if the absorption were not significant, a large difference between the impedances of the two media tends to reduce the amount of acoustic energy transmitted. Taking into account both premises at the same time, when a wave propagates by air and reaches a material

, Ft <sup>¼</sup> <sup>4</sup>Z1Z<sup>2</sup>

ð Þ Z<sup>1</sup> þ Z<sup>2</sup>

<sup>2</sup> (7)

when passing from a medium of acoustic impedance Z1 to another of acoustic impedance Z2. The relationship between the acoustic impedances does not only have to do with the modification of the amplitude of the incident wave: it is also related to the fraction of the incident energy that will be reflected or transmitted. Most of the acoustic properties of materials can be studied by the application of new laboratory and numerical methods as ultrasonic characterization [4], inverse characterization with basis on the acoustic impedance measurement [5], or ensemble

performance will decrease.

Acoustics of Materials

3. Sound insulation

poorly sealed, among other possible imperfections).

3.1 How does sound insulation occur?

phenomena, as the acoustic absorbers do.

of the impedances of the two media involved:

Fr <sup>¼</sup> <sup>Z</sup><sup>1</sup> � <sup>Z</sup><sup>2</sup> Z<sup>1</sup> þ Z<sup>2</sup> <sup>2</sup>

averaged scattering [6].

zero.

10

all the holes.

surface, most of the energy will be reflected, and only a small portion will be transmitted to the wall, as its acoustic impedance is undoubtedly much greater than that of air. When passing from the wall again to the air, most of the energy will be again reflected inside the wall, and only a small portion will be transmitted to the air. Then, the transmitted wave will have a smaller amplitude than the wave that would result if the propagation media has not changed (Figure 6).

The transmission coefficient τ of a material is then the relation between the transmitted energy and the incident energy:

$$
\pi = \frac{E\_t}{E\_i} \tag{8}
$$

The acoustic reduction index R is defined with basis on τ:

$$R = 10 \log \frac{1}{\tau} \tag{9}$$

### 3.2 Acoustic performance of a single wall

A single wall in acoustics is formed by only one foil. If it is a macroscopically homogeneous wall, its acoustic insulation will depend on several of its mechanical properties.

Intuitively, a simple and homogeneous wall offers good sound insulation when it is heavy and tight to the passage of air but only weakly rigid. A more rigorous analysis allows recognizing several zones with different behavior, as shown in Figure 7: the design zones are those controlled by mass or by coincidence; the zones controlled by stiffness or resonance refer to a poor and irregular acoustic performance.

Figure 6. Destinations of the acoustic energy that reaches a wall.

Figure 7. Acoustic performance of a simple homogeneous wall (adapted from [7]).

1. Stiffness-controlled zone: it corresponds to the lowest frequencies, below the frequency of resonance fr. The greater the stiffness k<sup>1</sup> , the poorer the insulation of the wall. The resonance frequency fres can be calculated as:

$$f\_{rs} = \begin{array}{c c} \frac{1}{2 \times \pi} \sqrt{\frac{E - e}{m \cdot S}} \end{array} \tag{10}$$

A more conservative expression is proposed by [1] to take into account the

4.Coincidence-controlled zone: it is the zone over the mass-controlled one. In general, the wall performance is similar to that at the mass-controlled one except when frequency is close to the coincidence or critical frequency fc. At this frequency, the bending waves that propagate in the material can coincide with the sound waves that propagate by the air, generating high amplitude vibrations in the wall. This phenomenon can occur above the so-called critical frequency fc, which is the one at which the frequency of the incident waves coincides with that of the longitudinal waves of bending of the wall. The insulation weakens, because the acoustic energy is transmitted through the divider in the form of bending waves, coupled with the acoustic waves in the air. This frequency depends exclusively on the material of the wall and its

where c is the speed of sound propagation in air, in m/s; e the thickness of the

From fc/2 onwards, the phenomenon of coincidence can occur. Then, fc/2 is often assumed as the limit of validity of the masses law. For frequencies higher than fc, the acoustic behavior is governed by the internal damping of the material; the insulation grows again from the value corresponding to fc. In this area, the law of mass is still used, although it is known that there is a very important drop in a frequency

If the critical frequency is expressed as a function of the resonance frequency, they turn out to be inversely proportional, so when selecting a partition with a low

<sup>f</sup> <sup>c</sup> <sup>¼</sup> <sup>0</sup>:<sup>0877</sup> <sup>c</sup><sup>2</sup>

The critical frequency is also inversely proportional to the stiffness k of the partition. The greater the stiffness is, the lower its critical frequency (and the higher

2

Table 1 presents the values of the Young and Poisson modules, the volumetric densities, and the critical frequencies for various materials, for a thickness of 1 cm. To obtain the critical frequency fc for other thicknesses, dividing the value of the

If the mass of an insulating element is doubled, the acoustic insulation improvement that can be achieved will be of a theoretical maximum of 6 dB, according to

).

fc ¼ 0:159c

efres

ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi m <sup>k</sup> <sup>1</sup> � <sup>υ</sup><sup>2</sup> ð Þ <sup>r</sup>

ffiffiffi S

TL ¼ 18 log m þ 18 log f –45 (12)

ð13Þ

(15)

; and E is the Young modulus of the

p (14)

irregularities and imperfections of the real materials:

thickness. The critical frequency is calculated as

wall, in m; m the surface density, in kg/m<sup>2</sup>

resonance frequency, it also has a high critical frequency:

table between the new thicknesses in cm is needed.

.

material, in N/m<sup>2</sup>

How Do Acoustic Materials Work?

DOI: http://dx.doi.org/10.5772/intechopen.82380

close to the critical frequency.

its resonance frequency):

3.3 Double walls

13

S is the area of the partition (m2

where m is the surface density2 of the material, kg/m2 ; e the thickness of the wall, in m; S the area of the wall, in m2 ; and E is the Young modulus of the material, in N/m2 .


The acoustic insulation performance of a simple homogeneous wall in the mass-controlled zone can be computed by the well-known expression of the masses law [4]:

$$\text{TL} = 20 \text{ log } m + 20 \text{ log } f \text{-42} \tag{11}$$

where m is the surface mass in kg/m<sup>2</sup> and f is the central frequency of the octave band in Hz.

<sup>1</sup> The stiffness k is the ability of a solid to withstand stresses without acquiring deformations. A wall can be idealized as a thin plate, so its flexural stiffness (i.e., the stress generated by a load perpendicular to it) can be expressed as <sup>k</sup> <sup>¼</sup> <sup>E</sup> <sup>1</sup>�ν<sup>2</sup> � <sup>e</sup><sup>3</sup> 12, where ν is Poisson's coefficient of the material.

<sup>2</sup> The surface density or surface mass of a material is the mass of 1 m<sup>2</sup> of it with its current thickness. Otherwise, m is the product of the volumetric density ρ of the material by its thickness e.

A more conservative expression is proposed by [1] to take into account the irregularities and imperfections of the real materials:

$$\text{TL} = \text{18 } \log m + \text{18 } \log f \text{--} 45\tag{12}$$

4.Coincidence-controlled zone: it is the zone over the mass-controlled one. In general, the wall performance is similar to that at the mass-controlled one except when frequency is close to the coincidence or critical frequency fc. At this frequency, the bending waves that propagate in the material can coincide with the sound waves that propagate by the air, generating high amplitude vibrations in the wall. This phenomenon can occur above the so-called critical frequency fc, which is the one at which the frequency of the incident waves coincides with that of the longitudinal waves of bending of the wall. The insulation weakens, because the acoustic energy is transmitted through the divider in the form of bending waves, coupled with the acoustic waves in the air. This frequency depends exclusively on the material of the wall and its thickness. The critical frequency is calculated as

$$f\_e = \frac{c^2}{\pi} \sqrt{\frac{3\,m}{E\,e^3}}\tag{13}$$

where c is the speed of sound propagation in air, in m/s; e the thickness of the wall, in m; m the surface density, in kg/m<sup>2</sup> ; and E is the Young modulus of the material, in N/m<sup>2</sup> .

From fc/2 onwards, the phenomenon of coincidence can occur. Then, fc/2 is often assumed as the limit of validity of the masses law. For frequencies higher than fc, the acoustic behavior is governed by the internal damping of the material; the insulation grows again from the value corresponding to fc. In this area, the law of mass is still used, although it is known that there is a very important drop in a frequency close to the critical frequency.

If the critical frequency is expressed as a function of the resonance frequency, they turn out to be inversely proportional, so when selecting a partition with a low resonance frequency, it also has a high critical frequency:

$$f\_c = 0.0877 \,\frac{c^2}{\text{ef}\_{res}\sqrt{\text{S}}} \tag{14}$$

S is the area of the partition (m2 ).

The critical frequency is also inversely proportional to the stiffness k of the partition. The greater the stiffness is, the lower its critical frequency (and the higher its resonance frequency):

$$f\_c = 0.159c^2 \sqrt{\frac{m}{k} \frac{m}{(1 - \nu^2)}}\tag{15}$$

Table 1 presents the values of the Young and Poisson modules, the volumetric densities, and the critical frequencies for various materials, for a thickness of 1 cm. To obtain the critical frequency fc for other thicknesses, dividing the value of the table between the new thicknesses in cm is needed.

#### 3.3 Double walls

If the mass of an insulating element is doubled, the acoustic insulation improvement that can be achieved will be of a theoretical maximum of 6 dB, according to

1. Stiffness-controlled zone: it corresponds to the lowest frequencies, below the

ffiffiffiffiffiffiffiffiffi E e m S

r

2 π

2. Resonance-controlled zone: it occurs between fres and 2 fres. In this zone, the behavior is irregular and unpredictable; points of very poor performance are

3.Mass-controlled zone: it is the preferred zone for acoustic design. It covers from 2 fres to half of the critical or coincidence frequency fc. The insulation depends on the surface mass and the frequency of the incident wave. It is usually computed according to the so-called masses law. An improvement of insulation of about 5.4–6 dB is expected each time frequency or mass duplicates. Close to the extremes of this zone, the wall insulation performance is rather poor. The acoustic insulation performance of a simple homogeneous wall in the mass-controlled zone can be computed by the well-known expression of the

where m is the surface mass in kg/m<sup>2</sup> and f is the central frequency of the

<sup>1</sup> The stiffness k is the ability of a solid to withstand stresses without acquiring deformations. A wall can be idealized as a thin plate, so its flexural stiffness (i.e., the stress generated by a load perpendicular to it)

<sup>2</sup> The surface density or surface mass of a material is the mass of 1 m<sup>2</sup> of it with its current thickness.

Otherwise, m is the product of the volumetric density ρ of the material by its thickness e.

12, where ν is Poisson's coefficient of the material.

, the poorer the insulation

; e the thickness of the wall,

; and E is the Young modulus of the material, in

TL ¼ 20 log m þ 20 log f –42 (11)

(10)

frequency of resonance fr. The greater the stiffness k<sup>1</sup>

Acoustic performance of a simple homogeneous wall (adapted from [7]).

where m is the surface density2 of the material, kg/m2

in m; S the area of the wall, in m2

alternated with others that are quite good.

N/m2 .

Figure 7.

Acoustics of Materials

masses law [4]:

octave band in Hz.

<sup>1</sup>�ν<sup>2</sup> � <sup>e</sup><sup>3</sup>

can be expressed as <sup>k</sup> <sup>¼</sup> <sup>E</sup>

12

of the wall. The resonance frequency fres can be calculated as:

fres <sup>¼</sup> <sup>1</sup>


Double walls have a good acoustic performance for the frequencies between

The resonance frequency will be lower the greater the masses of the two foils and/or the greater the distance between them. When the air chamber between the two foils of the double wall is filled with absorbent material, the resonance frequency of the whole decreases (about 85 % of the calculated value). The desirable values for fres are less than 100 Hz and as an optimum condition, less than 60 Hz. Close to the resonance frequency, the insulation is very poor; hence, it should be lower than the most probable minimum incidence frequencies (for human speech they can typically be up to 80 Hz and for music, even lower than 40 Hz). For frequencies below fres, the behavior of the set of the double wall is, at most, that of a simple wall with a surface mass equal to (m1+m2), although its performance could

The end of the range in which the double wall has its best performance occurs at its critical frequency fc, which does not depend on the masses of the partitions but

Every time d equals a whole number of half wavelengths, the acoustic insulation has an important decay. This occurs at the harmonic frequencies of fc. For these frequencies, stationary waves of n.fc frequencies (n = 1, 2, 3, ...) occur in the air

Stationary waves are periodic waves where the nodes and crests occupy fixed positions that do not vary in time. Because d is an integer multiple of λ/2, a node will occur on the second foil of the double wall, and the wave will be reflected with very little energy dissipation, with at least one relative maximum remaining in the air chamber. To attenuate this deleterious effect, absorbent material can be placed on one side of the cavity. This not only improves the insulation of the set by dissipating acoustic energy but also improves its acoustic performance by lowering its reso-

As practical criteria, if the double partition is composed of two light, flexible

Also, the air chamber might contain a nonrigid porous absorbent material. Predicting the acoustic insulation of a double wall is not obvious, because of the different phenomena involved in its performance. Referring to laboratory tests is hardly recommended. Table 2 shows some results from laboratory tests of double walls. Sometimes not only double walls are used but also three-foiled walls. The involved acoustic phenomena are so complex that laboratory testing is mandatory

Although when the calculations are rightly performed, there are some factors

ð17Þ

ð18Þ

, then the distance d between

their resonance frequency and their critical frequency.

be poorer.

nance frequency.

15

sheets must comply with

only on the distance d between them:

How Do Acoustic Materials Work?

DOI: http://dx.doi.org/10.5772/intechopen.82380

chamber, which further weaken the insulation.

sheets of surface masses m1 and m2 expressed in kg/m<sup>2</sup>

to determine their acoustic insulation performance.

3.4 Some causes that weaken the acoustic performance of a wall

that can make the forecasts much more optimistic than the actual acoustic

#### Table 1.

Density and critical frequency of some materials (from different sources).

masses law. But if the mass increase is done by distributing it in two not linked elements separated by an air chamber, the performance of the whole is better than that which results simply from doubling the mass of the original element. This is due to the changes in acoustic impedance to which the sound waves are undergoing when passing through the different elements of the set. The acoustic performance is further improved if the two elements are not exactly the same, and it can be even better if a sound absorbent material is placed into the air chamber.

It is very important to meet a real constructive independence between both foils of the wall, since otherwise the whole will not work as a double wall but simply as a wall whose mass is the sum of the masses of the two elements. Distributing nonhomogeneously the total mass is advantageous, since it allows to achieve that both partitions have different critical and resonance frequencies, avoiding the occurrence of frequencies for which the overall performance would be very poor. If the two wall foils are rigidly joined, the insulation of the whole will decrease. If a reasonably independence is constructively achieved (i.e., they do not vibrate together), the resonance frequency of the overall turns out to be

$$f\_r = 60\sqrt{\frac{1}{d} \left(\frac{1}{m\_1} + \frac{1}{m\_2}\right)}\tag{16}$$

where m1 and m2 are the surface masses of both elements, in kg/m<sup>2</sup> ; and d is the thickness of the air chamber or separation between partitions, in m.

Double walls have a good acoustic performance for the frequencies between their resonance frequency and their critical frequency.

The resonance frequency will be lower the greater the masses of the two foils and/or the greater the distance between them. When the air chamber between the two foils of the double wall is filled with absorbent material, the resonance frequency of the whole decreases (about 85 % of the calculated value). The desirable values for fres are less than 100 Hz and as an optimum condition, less than 60 Hz. Close to the resonance frequency, the insulation is very poor; hence, it should be lower than the most probable minimum incidence frequencies (for human speech they can typically be up to 80 Hz and for music, even lower than 40 Hz). For frequencies below fres, the behavior of the set of the double wall is, at most, that of a simple wall with a surface mass equal to (m1+m2), although its performance could be poorer.

The end of the range in which the double wall has its best performance occurs at its critical frequency fc, which does not depend on the masses of the partitions but only on the distance d between them:

$$f\_e = \frac{c}{2d} \tag{17}$$

Every time d equals a whole number of half wavelengths, the acoustic insulation has an important decay. This occurs at the harmonic frequencies of fc. For these frequencies, stationary waves of n.fc frequencies (n = 1, 2, 3, ...) occur in the air chamber, which further weaken the insulation.

Stationary waves are periodic waves where the nodes and crests occupy fixed positions that do not vary in time. Because d is an integer multiple of λ/2, a node will occur on the second foil of the double wall, and the wave will be reflected with very little energy dissipation, with at least one relative maximum remaining in the air chamber. To attenuate this deleterious effect, absorbent material can be placed on one side of the cavity. This not only improves the insulation of the set by dissipating acoustic energy but also improves its acoustic performance by lowering its resonance frequency.

As practical criteria, if the double partition is composed of two light, flexible sheets of surface masses m1 and m2 expressed in kg/m<sup>2</sup> , then the distance d between sheets must comply with

$$d \cdot \begin{bmatrix} m \end{bmatrix} \ge \begin{cases} \frac{1}{m\_1} + \frac{1}{m\_2} \end{cases} \tag{18}$$

Also, the air chamber might contain a nonrigid porous absorbent material. Predicting the acoustic insulation of a double wall is not obvious, because of the different phenomena involved in its performance. Referring to laboratory tests is hardly recommended. Table 2 shows some results from laboratory tests of double walls.

Sometimes not only double walls are used but also three-foiled walls. The involved acoustic phenomena are so complex that laboratory testing is mandatory to determine their acoustic insulation performance.

#### 3.4 Some causes that weaken the acoustic performance of a wall

Although when the calculations are rightly performed, there are some factors that can make the forecasts much more optimistic than the actual acoustic

ð16Þ

; and d is the

masses law. But if the mass increase is done by distributing it in two not linked elements separated by an air chamber, the performance of the whole is better than that which results simply from doubling the mass of the original element. This is due to the changes in acoustic impedance to which the sound waves are undergoing when passing through the different elements of the set. The acoustic performance is further improved if the two elements are not exactly the same, and it can be even

Poisson modulus ν, N/m<sup>2</sup> � <sup>10</sup><sup>10</sup>

2.61 � <sup>10</sup><sup>10</sup> – <sup>2600</sup> <sup>1900</sup>

1.50 � 1010 – <sup>1090</sup> <sup>1700</sup>

<sup>7</sup> � 109 – <sup>750</sup> <sup>2700</sup>

– – 33 10,900

Solid bricks 2.50 � <sup>10</sup><sup>10</sup> – <sup>2000</sup> <sup>2700</sup>

Steel 1.95 � 1011 0.31 <sup>7800</sup> <sup>1300</sup> Aluminum 7.16 � 1010 0.4 <sup>2700</sup> <sup>1200</sup> Lead 1.58 � <sup>10</sup><sup>10</sup> 0.43 11,300 <sup>5500</sup>

Gypsum 4.69 � <sup>10</sup><sup>9</sup> – <sup>1150</sup> <sup>2700</sup> Plasterboard – – 875 4600 Glass 6.76 � <sup>10</sup><sup>10</sup> 0.22 <sup>2500</sup> <sup>1200</sup> Pinus wood 1.40 � 1010 0.18 <sup>700</sup> <sup>1700</sup>

Plywood – – 600 2100 Cork <sup>5</sup> � <sup>10</sup><sup>6</sup> 0.28 <sup>250</sup> 18,000 Rubber <sup>7</sup> � <sup>10</sup><sup>6</sup> 0.4 <sup>1100</sup> 85,000

Density (kg/m<sup>3</sup> ) Critical frequency for 1 cm thickness (Hz)

It is very important to meet a real constructive independence between both foils of the wall, since otherwise the whole will not work as a double wall but simply as a

better if a sound absorbent material is placed into the air chamber.

Density and critical frequency of some materials (from different sources).

Young modulus E, N/m<sup>2</sup> � <sup>10</sup><sup>10</sup>

Reinforced concrete

Acoustics of Materials

Asbestos cement

Agglomerated wood

Extruded polystyrene

Table 1.

14

together), the resonance frequency of the overall turns out to be

wall whose mass is the sum of the masses of the two elements. Distributing nonhomogeneously the total mass is advantageous, since it allows to achieve that both partitions have different critical and resonance frequencies, avoiding the occurrence of frequencies for which the overall performance would be very poor. If the two wall foils are rigidly joined, the insulation of the whole will decrease. If a reasonably independence is constructively achieved (i.e., they do not vibrate

where m1 and m2 are the surface masses of both elements, in kg/m<sup>2</sup>

thickness of the air chamber or separation between partitions, in m.


4. Acoustic diffusion

How Do Acoustic Materials Work?

DOI: http://dx.doi.org/10.5772/intechopen.82380

modes of a room.

interferences [11].

one frequency octave.

different depths.

17

The diffusion of sound is a consequence of the multiple reflections and diffractions that it suffers on irregular surfaces or obstacles to propagation. The diffusers are used to achieve a homogeneous sound field by scattering the reflected acoustic energy in all directions. When a diffuse field is achieved, the acoustic energy is

The diffusers allow to correct the early and late reflections and the normal

The design of the surface irregularities can be computed according to different numerical sequences with basis on the main principles of acoustic wave

pattern. As a consequence, a good acoustic energy scattering is achieved.

The most frequent design methods are presented below.

1. MLS diffusers (maximum length sequence)

Unlike the systems of isolation and absorption, in which the most important are the characteristics of the material, the diffusers can be built in any material provided a proper surface design. When a good spatial distribution is achieved, a good

They are usually built as a sequence of thin linear apertures with different depths. The sound waves penetrate the material, experiment many reflections into the apertures, and emerge from them with a different phase, that is, in a different interference

The so-called geometric Schroeder's diffusers or RPG diffusers (reflection phase

They are designed using a periodic number sequence that decides the position of the apertures on the surface of the material. If the width of the irregularities is reduced, the design frequency of the diffuser will be higher, while if the depth will be higher, the frequencies to be corrected will be lower. The width of the openings is λ/2 and the depth is λ/4. This kind of diffusers has a good performance only for

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

They have linear openings of different depths, but they do not suit a periodic

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

grating) can be modified in order to be used as acoustic absorbers (Schroeder's absorbers) [12]. Caution is needed to avoid obtaining an undesired behavior (sound

homogeneously and isotropic distributed both in space and in time.

temporary dispersion is usually achieved as well.

4.1 Phase diffusers (Schroeder's diffusers)

absorption instead of sound diffusion).

2. QRD (quadratic residue diffusers)

3.PRD (primitive root diffusers)

4.2 Crystal-structured diffusers

pattern because of the number sequence used for the design.

#### Table 2.

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

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

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 the acoustic insulation of the wall.

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 solution.
