2.2 Membrane or plate absorbers

A membrane or plate absorber is an air impervious material fixed at its edges at a certain distance from a rigid surface, so as to leave a tight cavity between both (Figure 4). When the stiffness of the material is negligible in relation to the tensions that hold it, it is said to be a membrane; when its stiffness must be considered, the material is said to be a plate.

The best performance of the plate is expected to occur at its resonance frequency and can be calculated as

$$f\_r = \frac{60}{\sqrt{md}}\tag{5}$$

In any case, the value of α coefficient of these plates is usually not more than 0.50. Since the surface mass of the panels has a practical minimum, these absorbers are useful only at low frequencies. Increasing the mass m of the panel or the distance d lowers the resonance frequency. If the cavity is filled with a soft material, the operating range broadens in terms of frequencies, but in turn it lowers the

The acoustic resonators consist of a cavity that communicates with the outside by a narrower conduit or neck, and of such dimensions they can dissipate energy in

The resonance frequency of a Helmholtz-type resonator can be calculated as follows:

; and l is the effective length of the neck of the resonator, in m: le =

ð6Þ

; V the inside volume of the

a certain frequency, that is, its resonance frequency (Figure 5).

where S being the neck area of the resonator, in m<sup>2</sup>

lreal + 1.7 r; r the radius of the neck, in m.

Outline of a Helmholtz acoustic resonator (adapted from [1]).

maximum value of α of the plate.

2.3 Resonator absorbers

Typical acoustic absorbent panel.

How Do Acoustic Materials Work?

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

Figure 4.

resonator, in m<sup>3</sup>

Figure 5.

9

where m is the surface mass of the plate, in kg/m<sup>2</sup> ; and d is the distance from the panel.

How Do Acoustic Materials Work? DOI: http://dx.doi.org/10.5772/intechopen.82380

#### Figure 4. Typical acoustic absorbent panel.

In any case, the value of α coefficient of these plates is usually not more than 0.50. Since the surface mass of the panels has a practical minimum, these absorbers are useful only at low frequencies. Increasing the mass m of the panel or the distance d lowers the resonance frequency. If the cavity is filled with a soft material, the operating range broadens in terms of frequencies, but in turn it lowers the maximum value of α of the plate.

#### 2.3 Resonator absorbers

The acoustic resonators consist of a cavity that communicates with the outside by a narrower conduit or neck, and of such dimensions they can dissipate energy in a certain frequency, that is, its resonance frequency (Figure 5).

The resonance frequency of a Helmholtz-type resonator can be calculated as follows:

$$f\_{\rm res} = \frac{c}{2\,\pi} \cdot \sqrt{\frac{S}{VI\_e}}\tag{6}$$

where S being the neck area of the resonator, in m<sup>2</sup> ; V the inside volume of the resonator, in m<sup>3</sup> ; and l is the effective length of the neck of the resonator, in m: le = lreal + 1.7 r; r the radius of the neck, in m.

Figure 5. Outline of a Helmholtz acoustic resonator (adapted from [1]).

Design and Faculty of Engineering) that demonstrated good acoustic performance and very low manufacturing cost, in addition to allowing the recycling of a very

Acoustic absorbers made with weaving wastes. Up: suspended mounting. Down: experimental absorption

A membrane or plate absorber is an air impervious material fixed at its edges at a

The best performance of the plate is expected to occur at its resonance frequency

ð5Þ

; and d is the distance from the

certain distance from a rigid surface, so as to leave a tight cavity between both (Figure 4). When the stiffness of the material is negligible in relation to the tensions that hold it, it is said to be a membrane; when its stiffness must be

common waste in Uruguay [3].

coefficient for different ways of mounting.

and can be calculated as

panel.

8

Figure 3.

Acoustics of Materials

2.2 Membrane or plate absorbers

considered, the material is said to be a plate.

where m is the surface mass of the plate, in kg/m<sup>2</sup>

#### Acoustics of Materials

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 performance will decrease.

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

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

The transmission coefficient τ of a material is then the relation between the

<sup>τ</sup> <sup>¼</sup> Et Ei

<sup>R</sup> <sup>¼</sup> 10 log <sup>1</sup>

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

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

Intuitively, a simple and homogeneous wall offers good sound insulation when it

(8)

<sup>τ</sup> (9)

will be again reflected inside the wall, and only a small portion will be

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

transmitted energy and the incident energy:

How Do Acoustic Materials Work?

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

3.2 Acoustic performance of a single wall

(Figure 6).

properties.

performance.

Figure 6.

11

Destinations of the acoustic energy that reaches a wall.

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 all the holes.
