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A Brief Review on Sound Absorption Characteristics of

Nonwoven Structures

Jagannath Sardar

(2008TTZ8165)

Department of Textile Technology

Indian Institute of Technology Delhi

New Delhi 110016

December 11, 2008

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Abstract: For a healthy and a pleasant environment, controlling the sound hazards is an important issue.

It is medical evidence, that the human body will takes sound as “pollution” if the ambient sound

levels exceed 65dB. This sound pollution leads to significant health problems including

hypertension, dizziness, depression, and most commonly, loss of hearing [1, 2].Noise control and

its principles play an important role in creating an acoustically pleasing environment. This can be

achieved when the intensity of sound is brought down to a level that is not harmful to human

ears.

Various techniques have been developed by using different materials to make a pleasing

environment. The sound absorbing materials absorbs the sound energy and it converts to the

thermal energy when the sound wave strikes the fibers assembly. This process is called an energy

conversion process. Many research papers revealed that the fibrous materials (textile) have a

good affinity to absorb the sound energy [3, 6, 8]. The porous materials can reduce the acoustic

energy of a sound wave as the wave passes through it by the phenomenon of absorption.

Acoustic porous materials can have porosity greater than 90%. Common sound absorptive

materials have open cells, which is called pores [4, 5, 7]. Foam and fibre assembly like

nonwovens are basically known as porous materials and it has been observed that those materials

have good sound absorption property. In some cases wood and composite materials are also be

used as a sound absorptive and barrier materials. For porous and fibrous materials, acoustic

performance is defined by a set of experimentally determined constants namely: absorption

coefficient, reflection coefficient, acoustic impedance, propagation constant, normal reduction

coefficient and transmission loss. These parameters are depends on some factors like fibre

diameter, fiber surface area, thickness, bulk density, porosity, airflow resistivity, tortuosity and

surface impedance.

In this report we have measured the noise absorption coefficient (NAC) and noise reduction

coefficient (NRC) of different nonwovens of polypropylene fibre in different thickness. It has

been found that the needle punched polypropylene has higher NAC value and it proves that NAC

value is higher in case of higher thickness [8, 42, 45].

In acoustic engineering, the sound absorptive materials have an important role according to its

applications, such as aeronautical industry, industrial noise control, room acoustics and

automotive and acoustics [16, 21].

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1. Introduction: A sound wave can be defined as the pattern of disturbance caused by the movement of energy

traveling through a medium (such as air, water, or any other liquid or solid matter) as it

propagates away from the source of the sound.

The vibration can be described as some object that causes disturbs the particles in the

surrounding medium; those particles disturb those next to them, and so on. Sound travels through

the air (gas), water (liquid) or brick (solid), as a pressurized longitudinal wave. In a longitudinal

wave the particle displacement is parallel to the direction of wave propagation. And transverse

wave the particle displacement is perpendicular to the direction of wave propagation [9].

The compressing and expanding of the air produces differences in air pressure. The pressure

differences in the air move away from the drum surface like ripples in a pond, creating a sound

wave. This is how the drum produces a sound that we can hear.

To generate sound, it is necessary to have a vibrating source, such as the tuning fork shown here.

When the source vibrates, it displaces adjacent particles and molecules in the medium, causing

them to vibrate back and forth as well. Their vibrations cause more distant particles to vibrate,

and so on. The audible sound that we hear is made up of tiny vibrations of air molecules, which

are transmitted to our ears. This transmission of vibrations, starting from the source and

continuing from one molecule to the next, is how sound travels through a medium [10].

Sound intensity is defined as the sound power per unit area. The usual context is the

measurement of sound intensity in the air at a listener's location. The basic units are watts/m2 or

watts/cm2 . Many sound intensity measurements are made relative to a standard threshold of

hearing intensity I0 [11]

Sound Intensity Level (dB) can be expressed by the intensity, since intensity is nothing but the

energy. It is expressed by [12]

When this level exceeds the limit 65 dB then it’s called Noise or Sound Hazards [1, 2].

The final expression for the acoustic intensity becomes [13],

).(Energy(E)

Area(a)Power(P)

I)Intensity(tatimeArea ⋅

==

)log(100II=β

3

where p = prms. We will show that this same expression also applies for a spherical sound wave

and for a non-spherical sound wave. The human ear can detect a wide range of sound intensities.

The decibel scale (dB) is commonly used to deal with the wide range in pressure, intensity,

power, and energy that are encountered in acoustics. Levels in decibels are defined using the

preferred SI reference quantities for acoustics in Table 1.1 (ISO 1683); these reference quantities

are used for all figures in the book [14].

Table 1.1 Sound – definitions of levels in decibels

Sound hazard system can be divided into three elements [13, 15], such as

1. Noise Source: The element which vibrates in a particular frequency and make noise hazards

in the air.

2. Noise Path: The medium through which the acoustical energy

propagates from one point to another and

3. Noise Receiver: The person who could potentially complain about the

quantity or level of noise as perceived at same point

Noise control and its principles play an important role in creating an acoustically pleasing

environment. This can be achieved when the intensity of sound is brought down to a level that is

not harmful to human health [30]. It is medical evidence, that the human body will takes sound

as “pollution” if the ambient sound levels exceed 65dB. This sound pollution leads to significant

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health problems including hypertension, dizziness, depression, and most commonly, loss of

hearing [1, 2]. From the early 10 decades, lots of considerable research and developments have

been done for dampening the sound intensity levels to control sound pollution. A various

application area of the noise reduction techniques [16, 17, 5, 18, 8] are as Aeronautical

Engineering, interiors of cars and public transport, hospital rooms, auditoriums, and laboratories

etc. Multi-layered panels are widely used in aircraft, automotive and building industries. The

sound transmission loss (TL) provided by the panels is an important factor in evaluating the

acoustical performance of such panels [19].

It is obvious that various techniques used to reduce the noise levels using different sound

absorbing materials [20, 21]. One reliable technique is to absorb the sound energy and converts

to thermal energy.

Different fibrous material such as different nonwoven textiles, porous foam, composite or other

materials are extensively used for the same aspects.

Many literatures reveals that nonwoven porous materials have a high impact characteristic to

absorb the sound energy [3, 24, 25, 26], hence, nonwovens have fibrous quantity and air. Due to

this combination, nonwovens absorb the sound energy and convert it to heat by the mechanism

of thermodynamics and aerodynamics principle [6, 22, 23].

2. Materials for sound absorption: Sound absorptive materials can be classified into three categories such as absorptive materials,

Barrier materials and damping material. [27]. These sound absorptive materials can be included

rugs, carpet with felt pads, heavy drapes etc. [28] The sound wave passes through the porous and

fibrous structural materials which transfer the aerodynamics energy to thermodynamics by the

phenomenon of absorption [27 ]. These materials are mostly used to control the acoustic

environment by dampening the sound energy of the resultant waves which is called reflective

wave. If the incident wave is a plane wave, and the structural properties of the slab do not change

in the direction of wave propagation, the transmitted wave will also be a plane wave traveling in

the same direction as the incident wave [7]. Absorptive materials are generally resistive in

nature, either fibrous, porous or in rather special cases reactive resonators [27]. Classic examples

of resistive material are nonwovens, fibrous glass, mineral wools, felt and foams. Porous

materials used for noise control are generally categorized as fibrous medium or porous foam.

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Fibrous media usually consists of rock wool or glass, polyester fibers and have high acoustic

absorption. Sometimes fire resistant fibers are also used in making acoustical products [29, 30].

Kannan Allampalayam Jayaraman [30] obtained his ms research preparing the nonwoven

samples, in needle punched and thermally bonded process, using kenaf fibre and PET in different

blend percentage. He explained and shows that the materials which he has used are efficient for

noise absorption.

Often sound barriers are confused with sound absorbing materials. Generally materials that

provide good absorption are poor barriers. K.O.Ballagh [8] explained that the acoustical

properties, i.e. Barriers and damping of the materials, the mass of the material, do not depend

strongly on the flow resistivity, and so, provided that it is within +20% of the desired value, the

acoustical properties should be maintained.no direct effect on the performance of the absorptive

materials [8]. Some of the acoustical fibric which are available in the market, has shown bellow

[fig. 2.1(a), 2.1(b)].

(a) (b)

Figure 2.1 (a) CrossPoint™ Acoustical Wall Fabric and b) EcoSorpt™ Recycled Cotton Panels

Michael Coates and Marek Kierzkowsld [31] explained that, bulk porous absorbers, such as

fiberglass or mineral wool batts or blankets, and needle punched, resin or thermally bonded

fibrous textiles, are well known and all qualify as rigid porous absorbers. Flow resistive screens

can provide similar performance to the high-loft materials, without the bulk. Thin lightweight

acoustic textiles, such as INC Engineered Materials Deci-Tex range, act as flexible porous

screens. They also said, for porous fibrous sound absorbers, it has been demonstrated that the

flow resistance is a function of density. Fibre packing density decreases the air permeability,

with a resultant increase in pressure drop and hence flow resistance. For increased sound

absorption at a given thickness, a higher-density fibrous material is used. [31]

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An absorber, when backed by a barrier, reduces the energy in a sound wave by converting the

mechanical motion of the air particles into low grade heat. This action prevents a buildup of

sound in enclosed spaces and reduces the strength of reflected noise [27].

David Frankovich [32] has shown that the porous nature of absorptive materials renders them

susceptible to contamination, moisture retention and deterioration due to physical abuse. To

avoid these problems, facings may be attached to at least one side of the absorber.

Figure 2.2 Performance of Various 1-inch Acoustical Foams with Surface Treatments

The addition of a facing to acoustical foam has the effect of increasing the lower frequency

absorption at the expense of the higher frequencies [32]. Later on we will discus regarding the

performance of absorptive materials which depends on some parameters of the used samples. 3. Influence of different factors for Sound absorption characteristics of

fibrous materials: Many literatures have revealed that how the different factors influenced to the characteristics of

sound absorption of the fibrous assembly [33, 3, 8, 6, 34]. A porous material with a non-porous

barrier bonded to the face of the material carries the sound energy in the form of the structure-

borne wave. The factors that have a strong influence on the structure-borne wave are the bulk

stiffness and the structural loss factor. For most porous materials, noise absorption coefficient

generally depends on such three factors as: flow resistance, porosity, morphology of pores, etc.

[35]. Summary from some literatures are cited below.

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3.1. Fibre diameter:

Young Joo Na, Jeff Lancaster, John Casali and Gilsoo Cho [36] has explained that the microfiber

fabric has fine fibres and a high surface area and it has been used in such applications as wipers,

thermal insulator, filters or breathable layers. It can be also used for sound absorption. They have

taken five microfibre fabrics of polyester and nylon in different blend percentage and one regular

fibre fabric of 100% polyester for the reverberation room method. The results showed that the

micro-fibre fabrics’ sound absorption is superior to that of conventional fabric with the same

thickness or weight, and the micro-fibre fabrics’ structure was found to be important for

controlling sound absorption according to sound frequency. In the given table (3.1) shows the

NRC(Noise Reduction Coefficient) changes with frequency.

Table 3.1 Sound absorption coefficients of micro-fiber fabrics and fleece.

From the table we can see that the NRC is higher in case of microfibre fabrics than the regular

fabric (fleece fabric).

Youneung Lee and Changwhan Joo [33] explained that the NAC of the sample is proportional to

the in the fine fibre contents upto a certain frequency range[37]. Increasing the frequency beyond

1500 Hz, NAC curve shows no clear tendency with fine fibre content. Youneung Lee et al. have

used 3 different parametric recyled polyester fibres like 1.2, 2, 7 denier and 38mm length and for

bond purpose 6 denier, 42 mm low melting polyester fibre in different percentage.

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Figure 3.1 Effect of fine fibre contents on sound absorption properties

K. A. Jayaraman [30] has observed that the finer size PET absorbs more sound than other fibers.

This is because finer linear density allows more fibers per volume (fig. 3.1, fig. 3.2), more

contact area and more tortuous channels allowing more absorption. Moreover fine fibers move

relatively more easily than coarser fibers which causes finer fibers to convert acoustic energy

into heat more easily than coarser fibers.

Figure 3.2 Sound absorption of fabric made from100% PET fibers of varying cross sections

From the above fundamentals, fine denier fibres have better sound absorbing properties than

coarse denier fibers. Super fine fibres have good sound absorption characteristics [8]. Absorption

of the energy of plane acoustic waves is different in the low and high frequency bands [38].

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3.2 Fiber surface area:

One of the important factor which influence the sound absorption characteristics of the materials

is fibre surface area. More finer fibres means more surface area.

The relation between the total surface area S (cm2) of fibers constituting a fiber assembly of

porosity Pe (%) and T (cm) is shown as follows:

S = a Tb x 104

where a and b are constants and T is the thickness. A fiber assembly which meets this equation

has the maximum sound absorption coefficient at a certain frequency, if it has no back air space

or at an optional frequency if it has a back air space suited to the frequency [39]. If samples are

uniform in thickness, the total surface area of fiber at Pe is constant, irrespective of the fineness

of fibers. This means that the relation between the fineness of fibers d (denier) and Pe (%) for a

sample of uniform thickness is shown thus,

(100-Pe) d-1/2 = constant

Pe for a sample made up of fibers of differing in denier is easily calculable by using this

equation. In a porosity range higher than Pe, the maximum absorption coefficients of samples

composed of fibers differing in fineness but arranged to be the same in total surface area do not

agree completely [39].

Kyoichi et al. and Narang et al. [40, 41] indicated a direct correlation between sound absorption

and fiber surface area. Their study explained the fact that friction between fibers and air

increases with fiber surface area resulting in a higher sound absorption. Kyoichi et al. observed

that the sound absorption coefficient rises as the fibre surface area of the sound-absorbing

materials increases (fig. 3.3(a) & fig. 3.3(b)).

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(a) (b)

Figure 3.3 (a) Sound absorption comparison for various fibres with frequency.

(b) surface area for various fibre-based sound-absorbing materials.

This can be explained by the fact that friction between the fibres and the air increases with a

larger fibre surface area, resulting in a higher sound absorption coefficient. Moreover it has been

said that, in the frequency range 1125 Hz – 5000 Hz, fibers with serrated cross sections absorb

more sound compared to ones with round cross sectional area.

The fabric weight would then become less important than fabric thickness as fabric lightness can

be achieved by using a micro-fiber fabric, which has less weight due to its large surface area.

Therefore these possibilities of micro-fiber fabrics were tested for their application as sound-

absorbing materials. As a result, micro-fiber fabrics (except those with a mesh structure)

absorbed all sound frequencies better than a conventional fabric, and also better than the data

from other studies of absorbing materials. Micro-fiber fabrics absorb sound better because their

fibers have a higher surface area than those of regular fiber fabrics, resulting in higher flow

resistance [36].

3.3 Thickness:

Many literature have cited that sound absorption in porous materials have concluded that low

frequency sound absorption has direct relationship with thickness. The effectiveness of

absorption is directly related to the thickness of the material [32]; absorbers are most effective

when their thickness is between one-fourth and one-half the wavelength of the sound, with the

maximum performance where the thickness is one-fourth the wavelength [5]. Masataka

Hakamada et al. [42] shows that the sound absorption coefficient increased with increasing

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specimen thickness at all frequencies (fig. 3.4 a). Not only that, the air gap, from specimen to the

rigid wall, has an importance to sound absorption too (fig. 3.3 b).

Fig. 3.4 (a) Effect of specimen thickness on sound absorption coefficient

(b) Effect of air-gap interval on the sound absorption coefficient [42]

A study by M.A. Ibrahim et al [43] showed the increase of sound absorption only at low

frequencies, as the material gets thicker. However, at higher frequencies thickness has

insignificant effect on sound absorption. When there is air space inside and behind the material,

the maximum value of the sound absorption coefficient moves from the high to the low

frequency range [42]. Another work has done by Kazuhiko Kosuge et al [44]. They also shows

for the lower frequency of the normal incidence wave, sound absorption increased by increasing

the thickness of the nonwoven (fig. 3.5).

Figure 3.5 Nonwoven thicknesses vs. normal incidence sound absorption

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3.4 Bulk density:

Numerous works has been done to study the influence of the bulk density on the sound absorbing

properties of fibrous materials. K.O.Ballagh [8] has shown the effect on NAC is quite significant

for bulk density, thickness and flow resistivity in the frequency range of 500 - 2000Hz for 25

mm thickness and 250-1000Hz for 100 mm thickness. He explains that within the frequency

range of 500-2000Hz, the NAC is proportionally higher with the higher bulk density, thickness

and higher flow resistivity (fig. 3.6).

Figure 3.6 absorption coefficients showing the effect of density and flow resistivity.

There is a close relationship between flow resistivity [45, 5], density and fibre diameter. It can be

seen that the flow resistivity generally increases with increasing density [46]. Additional tests

have done on a single sample with a particular fibre diameter which was compressed to various

degrees, and the flow resistivity can be measured over a range of different.

K.O.Ballagh [8] explained that the flow resistivity is inversely proportional to the fibre diameter

and proportional to the density of the sample.

Energy loss increases as the surface friction increases, thus the sound absorption coefficient

increases.

3.5 Porosity:

Porosity is relatively important factors which prominently influenced to the Sound absorption

characteristics of porous materials [47]. The fig. 3.6 shows the influence of porosity along with

the bulk density on sound absorption coefficient of the porous materials.

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Figure 3.6 Sound absorption characteristics of 2.5 cm thick sample

Da: Observed apparent density and P: Porosity

Already we have seen that many factors have the influence to sound absorption properties of the

porous materials. One of the important factor is porosity. To allow sound dissipation by friction,

the sound wave has to enter the porous material. This means, there should be enough pores on

the surface of the material for the sound to pass through and get dampened. The porosity of a

porous material is defined as the ratio of the volume of the air in the material to its total volume.

Definition of the porosity (�) [48, 49], we can write as,

� = 1- � = t

a

vv

where, � is the fibre volume fraction and va and vt are the volume of the air (void volume) and

total volume of the sample respectively.

A porous material such as nonwovens with an open face carries most of the sound energy in the

form of the airborne wave. The exception is a porous material that has a structural stiffness less

than that of air. In this case, the material behaves as a fluid. In either case, the sound energy can

be thought of as being carried by the airborne wave. There are several factors that have a strong

influence on the airborne wave, but usually the most important influence is due to the flow

resistivity of the material. Most of the materials tested in this study were porous materials with

an open or scrim covered face, so the airborne wave is dominant [5].

Shoshani et al. [50] considered that, four functional forms of the porosity: linear, quadratic,

exponential and logarithmic. He assume that, layer can be approximately thought of as a

combination of several thin layers; each of which having a constant porosity. Therefore, it seems

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to us that our generalized theory can be used as a tool for assessing the noise absorption capacity

of multilayer nonwoven structure.

According to the functional form of porosity, they reveals numerical configuration as,

a) Linear:

b) Quadratic:

c) Exponential:

and

c) Logarithmic:

Where, each of these forms depends on two parameters P1 and P2 satisfying 0< P1, P2<1;

� represents the thickness of the web. These functions can be increasing or decreasing with

respect to x, depending on the choice of the parameters P1 and P2 (P1, P2 the best fit parameters.)

3.6 Airflow resistivity:

Airflow resistivity is most important factor to characterize the sound absorption properties of the

fibrous materials. A number of researchers have shown the influence of airflow resistivity to

sound absorption behaviour of textile materials.

The air flow resustance R (pascal.s/m3) is defined as,

R = �p/qv

Where �p is the air pressure difference across a layer of porous material; with respect to the

atmosphere (Pa), and qv is the volumetric airflow rate passing through the layer (m/s).

The volumetric airflow rate is

qv = u.S.

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where u is the linear airflow velocity (m/s) and S is the cross sectional area of the porous

materials perpendicular to the direction of air flow (m2).

Now specific airflow resistance Rs (Pa.s/m) applies to a specific thickness of a porous material;

hence it is an appropriate specification parameter for both homogeneous and non homogeneous

materials as well as materials with a porous surface coating or perforated surface layer.

Rs = R.S

The airflow resistivity, r (pa.s/m2) is the specific airflow resistance per unit thickness, and is only

appropriate as a specification parameter for homogeneous materials.

R = S. �p/dqv

= R.S/d

= Rs/d

Where d is the thickness of the layer of porous materials in the direction of airflow (m) [14]

3.6.1 Flow Resistance Measurement Unit:

The schematic diagram of the set-up for flow resistance measurements of textile materials is

shown in Figure 3.7. The set-up comprises two circular columns 50 mm in diameter and

approximately 50 cm long (made of acrylic material), between which the textile sample is fixed

during experiments. A thin rubber gasket is placed on the textile to avoid leakage. A 50 L plastic

tank is used as water reservoir, and an Iwaki-MD6 pump (maximum output 38 Uminute) is used

to circulate water in the flow loop. The flow through the column (and hence through the textile)

is measured with help of two GF rotameters (one with a range of 5-50 L/hour and the other 30-

300 L/hour). The pressure difference across the textile sample is measured with a Honeywell

STD-120 differential pressure indicator [7]. In the fig. 3.7, a schematic diagram has been shown

for measuring the airflow resistivity of the materials.

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Figure 3.7 Schematic diagram of the experimental set-up for how resistance

measurements: (1) detachable columns to hold the textik. (2) textile sample. (3) pressure

transmitter with air locks. (4) rotameters, (5) pump. (6) water reservoir. (7) 3-waiy valve for

collecting samples for the analysis.

One of the most important factor that influence the sound absorbing characteristics of a

nonwoven material is the specific flow resistance per unit thickness of the material. The

characteristic impedance and propagation constant, which describes the acoustical properties of

porous materials, are governed to a great extent by flow resistance of the material [51, 5]

Now, acoustical properties are a function of both the density and the fibre diameter of the

sample. A more useful parameter for comparing different samples is the flow resistivity, since

different samples with the same flow resistivity (but different combinations of density and fibre

diameter) have similar acoustical properties. At higher values of airflow resistivity, there is some

improvement in low-frequency performance but at the expense of a reduction in high-frequency

absorption.

K. O. Ballagh [8] has shown that, there is a close relationship between flow resistivity, density

and fibre diameter. The flow resistivity has been plotted in fig. 3.8 acording to the density

(kg/m3) Vs. Flow resistivity (Rayls/m) , for the range of samples measured. It can be seen that

the flow resistivity generally increases with increasing density, although there is a reasonable

degree of scatter.

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Figure 3.8 Relationship between flow resistivity and density for all samples.

Fibers interlocking in nonwovens are the frictional elements that provide resistance to

acoustic wave motion. In general, when sound enters these materials, its amplitude is decreased

by friction as the waves try to move through the tortuous passages. Thus the acoustic energy is

converted into heat [52]. This friction quantity which can be expressed by resistance of the

material to airflow is called airflow resistance and is defined in equation as:

where: R1 = Specific flow resistance, mks Rayls/m

u = Particle velocity through sample, m/sec

� p = Sound pressure differential across the thickness of the sample

measured in direction of particle velocity, newtons/m2

� T = Incremental thickness

3.7 Tortuosity:

The most simple mathematic method to estimate tortuosity is arc-chord ratio: ratio of the length

of the curve (L) to the distance between the ends of it (C)[ 53]:

� = L/C

Arc-chord ratio equals 1 for a straight line and is infinite for a circle.

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Patasius, M. et al. [54] has given a generalized formula to measure tortuosity by an integral of

square of derivative of curvature, divided by the length of a curve

Where k’ is the derivatives of the curvature with respect to time.

Tortuosity is a measure of the elongation of the passage way through the pores, compared to the

thickness of the sample. According to Knapen et al. [55], tortuosity describes the influence of the

internal structure of a material on its acoustical properties. Con Wassilieff [56] describes

tortuosity as a measure of how far the pores deviate from the normal, or meander about the

material. It was stated that, K. V. Horoshenkov et al. [57] that, tortuosity mainly affects the

location of the quarter-wavelength peaks, whereas porosity and flow resistivity affect the height

and width of the peaks. It has also been said by the value of tortuosity determines the high

frequency behavior of sound absorbing porous materials.

As the porous layer has an initial thickness d0 [58], the porous layer undergoes a compression,

the thickness decreases to dn, which is the so-called final thickness. The compression rate n is

defined as the ratio of initial thickness to the final thickness after compression. Wave numbers

are related to the parameters, tortuosity, characteristic length, flow resistivity, porosity and

density. Compressing the material affects these parameters. So compression is an another

important factor. The new porosity, the flow resistivity, the tortuosity, the viscous characteristic

length and the thermal characteristic length caused by the compression, Bernard Castagnede et al

has shown the expression of tortusity as,

Where n nd

d0= (fig. 3.9)

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Figure 3.9 The illustration of compression rate.

Along with tortuosity, the inner structure of porous materials has been described by the term

‘structure factor’has given the approximate relation between porosity (�) and structure factor (K)

for homogenous materials made of fibers or granules with interconnecting pores. In the table

[55] shows how the tortuosity varied with some factors.

Table 3.1 Porosity, flow resistivity and tortuosity

3.8 Surface impedance:

The effect that a surface has on an acoustic wave can be characterized by four interrelated

acoustic quantities [59]: the impedance (z), admittance (� =1/z), the pressure reflection factor (R)

and the absorption coefficient (�). The first three (impedance, admittance and pressure reflection

factor) give information about both the magnitude and phase change on reflection. The

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absorption coefficient does not contain phase data, but only gives information about the energy

change on reflection.

The pressure reflection coefficient, R, gives the ratio of the reflected and incident pressure, i.e:

The pressure reflection coefficient therefore includes both magnitude and phase information

about the reflection of sound. (There is also an intensity reflection coefficient, but this is not used

here). The relationships between pressure reflection coefficient and impedance for oblique

incidence is:

where, � is the angle of incidence and is the density of the medium and c the speed of sound in

the acoustic medium. The ratio of pressure to velocity gives the characteristic specific acoustic

impedance of the medium, zc, and z1 is the surface impedance.

As the time response of the surface impedance is a sum of exponential functions, a recursive

implementation is possible. The infinite sum of exponentials in the time domain has to be

reduced to a finite number of terms. As a consequence, this approximation of the impedance

leads to a frequency-dependent error [60].

The higher the acoustic resistivity of a material, the higher is its dissipation, for a given layer of

thickness. At the same time the surface impedance of the layer also increases with resistivity,

resulting in a greater amount of reflections on the surface layer, giving a lower absorptivity

capability. Moreover the whole process is frequency dependent, so that for lower frequency

bands the necessary layer thickness increases as resistivity decreases [5].

The surface impedance seen [61] by a plane wave normally incident on a conductor is the same

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as that seen by a wave traveling parallel to the conductor, as in a transmission line. For simplicity

in the present discussion, we consider experiments in which a plane wave is normally incident on

the surface of the conductor or model under test (fig. 3.10).

Figure 3.10 Model diagram for surface impedance

The surface impedance is often split into the real term (resistance) and imaginary term

(reactance). In general, the real term of surface impedance is associated with energy losses, and

the imaginary term with phase changes. So a simple inspection of the surface acoustic impedance

can give more insight into the absorbing properties of a material than the absorption coefficient.

Remembering that the absorption coefficient, �, is a ratio of the absorbed and incident energy

enables the following expression to be derived:

The normal acoustic surface impedance, Za,n, is defined as the ratio of the complex sound

pressure at a surface, to the component of the complex sound particle velocity that is normal to

this surface [14],

Although we are mainly interested in plates (representing walls or floors) that form the room

boundaries, the above definition applies to any surface, including sheets of porous materials

such as mineral wool or foam.

The specific acoustic impedance, Za,s, is defined using the characteristic impedance of air,

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According to Frank Fahy, [62] normalized surface impedance (Z) can be calculated using the

equation,

where: = Air density (kg/m3)

c = Sound velocity in air (ms-1)

K. A. Jayaraman [30] has found out that the surface impedance increasing with increasing the

sample thickness. NAC is increasing with increasing the surface impedance upto 3500Hz.

4. The sound absorption spectrum: Zhang Xin’an [63] and Y.Shaoshani [64] has given a simple equation for calculating the Sound

Absorption Coefficient (SAC) for the fibrous materials.

He explain that, it is known that there are maximum SAC at D = n/ 4 (n=1, 3, 5….) and

minimum SAC at D= n/2. This is also the characters of stand wave in the tube. So, it is

reasonable to assume that the SAC of material in the stand wave tube is positive proportion with

the wave amplitude. That means high wave amplitude will cause high SAC and lower wave

amplitude will cause lower SAC. Let y denote the wave amplitude, then

Where, Y is the maximum amplitude, � is the angular frequency, let � = 0 and A = KY

then,

(� is the SAC)

For � = 2�f, =c/, (, c, denote frequency, sound speed and wave length respectively)

Then,

Let the back wall of the tube be the zero point, so,

23

This is the formula of sound absorption spectrum for fibrous material.

Zhang Xin’an [63] also explained that the increase of the wave amplitude of sound source will

not cause the change of SAC tested. The reason is that the higher wave amplitude of sound

source will cause the increase of both the maximum pressure P1 and the minimum pressure P2 in

stand wave tube, but the value of SAC is determined by P2/P1.

5. Mechanism of Sound Absorption in Fibrous Materials: Many scientists have explained the dissipation mechanism of sound absorption results from the

acoustic energy to heat [45, 65].

According to Randall F. Barron [13], the attenuation or dissipation of acoustic energy as a sound

wave moves through a medium may be attributed to three basic mechanisms:

(a) Viscous effects (dissipation of acoustic energy due to fluid friction), which result in

thermodynamically irreversible propagation of sound,

(b) Heat conduction effects (heat transfer between high- and low temperature regions in the

wave), which result in non-adiabatic propagation of the sound and

(c) Internal molecular energy interchanges (molecular energy relaxation effects), which result in

a time lag between changes in translational kinetic energy and the energy associated with

rotation and vibration of the molecules.

The attenuation due to the sum of the first two mechanisms, viscous and heat conduction is

called the classical attenuation.

Massimo Garai & Francesco Pompoli [46] have explained, the microstructural models provide a

deep physical insight of sound energy dissipation mechanisms into the porous materials. Sound

absorption mechanism is depends on some parameters, such as, number, size of pores,

morphology of the pores and fibre thermal conductivity [35].

With internal losses the sound energy is converted into heat [14]. Hence high internal loss factors

are beneficial for the noise control engineer who is trying to reduce sound levels. Internal losses

occur when the sound wave hits absorptive surfaces or objects (e.g. sound absorbent ceiling tiles,

carpet, porous materials) and as the wave travels through the air due to air absorption. The

24

former is usually more important than the latter because air absorption only becomes significant

at high frequencies and in large rooms.

Temperature variations associated with the passage of an acoustic disturbance through a gas next

to a solid boundary, which is characterized by a very much greater thermal capacity, will

likewise give rise to a thermal wave propagating into the boundary; but again, as with the shear

wave, the thermal wave will be confined to a very thin thermal boundary layer of the same order

of size as the viscous boundary layer. Such viscous and thermal effects, generally referred to as

the acoustic boundary layer, are usually negligible for energy transport, and are generally

neglected, except in the analysis of sound propagation in tubes and porous media, where they

provide the energy dissipation mechanisms [66].

According to Randall F. Barron, [13] the mechanism for absorption of acoustic energy for the

porous materials is the fluid frictional energy dissipation between the air and the solid fibers. At

high frequencies, the energy dissipation is larger because the particle velocity is larger than at

low frequencies. The expansion and contraction of the air within the irregular spaces of the

material also result in momentum losses for the air.

Figure 4.1 Surface absorption coefficient � for a porous felt-like material.

The results are illustrated in Fig. 4.1 that the absorption coefficients are larger for the thicker

material, which has more surface area for energy dissipation.

According to Malcolm J. Crocker et al. [67], have described the mechanism of sound absorption

happen by three ways,

25

1) A change in the flow direction of sound waves, together with expansion and contraction

phenomenon of flow through irregular pores, results in a loss of momentum

2) Air molecules oscillate in the interstices of the porous material with the frequency of the

exciting sound wave, results into frictional losses and

3) Air molecules in the pores undergo periodic compression and relaxation which results in

change of temperature. They have shown,

(a) (b)

Fig. 4.2 a) Sound propagation through porous sample and b) Viscous losses in air channels and

mechanical friction due to fiber rubbing

The mechanism of sound dissipation as: when sound enters porous materials, owing to sound

pressure, air molecules oscillate in the interstices of the porous material with the frequency of the

exciting sound wave. This oscillation results in frictional losses. A change in the flow direction

of sound waves, together with expansion and contraction phenomenon of flow through irregular

pores, results in a loss of momentum. Owing to exciting of sound, air molecules in the pores

undergo periodic compression and relaxation. This results in change of temperature. Because of

long time, large surface to volume ratios and high heat conductivity of fibers, heat exchange

takes place isothermally at low frequencies. At the same time in the high frequency region

compression takes place adiabatically. In the frequency region between these isothermal and

adiabatic compression, the heat exchange results in loss of sound energy. This loss is high in

fibrous materials if the sound propagates parallel to the plane of fibers and may account up to

40% sound attenuation [30].

26

D. A. Bies et al. [66] has also explained that, any propagating sound wave has both potential and

kinetic energy associated with it. The total energy (kinetic + potential) present in a unit volume

of fluid is referred to as the energy density. Energy density is of interest because it is used as the

quantity that is minimized in active noise cancellation systems for reducing noise in enclosed

spaces. The kinetic energy per unit volume is given by the standard expression for the kinetic

energy of a moving mass divided by the volume occupied by the mass.

K. A. Jayaraman [30] has mentioned in his MS thesis that, Fine fibre has high affinity to absorb

sound energy. This is because finer linear density allows more fibers per volume, more contact

area and more tortuous channels allowing more absorption. Moreover fine fibers move relatively

more easily than coarser fibers which causes finer fibers to convert more acoustic energy into

heat easily than coarser fibers.

6. Measurement of sound absorption coefficient: Many scientists have characterized the sound absorption property of the textile materials using

different techniques. Generally, textile materials can be characterized by measuring some

properties as, sound absorption coefficient (�), reflection coefficient (R), or surface impedance

(Z).

Massimo Garai [68] has mentioned the Measurement techniques used to characterize the sound

absorptive properties of a material are:

Impedance Tube Methods,

Steady State Methods and

Reverberant Field Methods

Yakir Z. Shoshani [3] has used the impedance tube technique to measure the noise absorption

coefficient of the textile materials.

The set-up (manufactured by Brüel and Kjaer Company of Denmark) [76] consists of a

cylindrical steel tube. The sample is fastened to the tube’s left wall, and a loudspeaker that can

emit sound waves of well defined frequencies is attached to its right wall. The nodes and

antinodes of the standing waves formed by the interference between the waves emitted by the

loudspeaker and those reflected from the sample are detected by a small microphone that can

slide along the axis of the tube. The diameter of the tube D is smaller than the wavelength of the

27

emitted sound wave (typically D = 10 cm for f < 800 Hz and D = 3 cm for f > 800 Hz) so that

this wave can be thought of as a plane wave propagating along the axis of the tube. The normal

incidence NAC of the specimen, designated by �, is defined by

where Io and I, are-the energy flux of the incident and reflected waves, respectively. If Pmin. is

the minimal sound pressure level in the tube and Pmax is its maximal value, a is given by

where n is the ratio between maximum pressure leve to minimum (Pmax/Pmin)

The amplitude or loudness of a sound wave is expressed by its sound pressure level. Sounds

having the same wavelength (equal frequency) may have differing loudness because the sound

pressure of a sound wave may vary over a wide range—a change in magnitude of ten million to

one—sound pressure is expressed using a logarithmic scale. This is the basis of the decibel scale,

which compresses the range of sound pressure into a scale from 0 to 150. The decibel (dB) is

not an actual measure of amplitude or loudness, but expresses the ratio between a given sound

pressure and a reference sound pressure. This relationship is expressed by the following

equation:

(Lp) = 10 log (P/Pre)2

where, Lp is the Sound Pressure Level, P is the Sound Pressure (Pa), Pre is the sound pressure at

the threshold of hearing (0.00002 Pa) [69].

28

6.1. Methods for acoustic measurements:

Impedance tube method uses plane sound waves that strike the material straight and so the

sound absorption coefficient is called normal incidence sound absorption coefficient, NAC (fig.

6.1) [70].

Figure 6.1 Impedance Tube for Sound Absorption

The impedance tube consists of a speaker, tube, two microphones and material sample holder. A

special sound called white noise is generated in the speaker. The white noise is composed of

sound contributions from all frequency bands in the audible range. The sound travels straight

down the tube and strikes the material. Some of the sound is absorbed and some is reflected

back. The two microphones measure the reflected sound. From the two microphone's signals, the

sound absorption can be calculated [70]. In an ITM (Impedance Tube Method) measurement (fig.

6.2), the acoustic waves are confined within the impedance tube, which is typically a few

centimeters in diameter, and the size of the materials sample need only be large enough to fill the

cross-section of the tube.[71].

29

Figure 6.2 Schematic Sketch of an Impedance Tube Set-Up [30]

Thus this method avoids the need to fabricate large test sample with lateral dimensions several

times the acoustical wavelength. The impedance tube method employs two techniques to

determine NAC, namely:

1. Movable microphone which is one-third octave frequencies technique (ASTM C 384) is

based on the standing wave ratio principle and uses an audio frequency spectrometer to measure

the absorption coefficients at various centre frequencies of the one-third octave bands.

2. Two-fixed microphone impedance tube or transfer function method (ASTM E 1050), which is

relatively recent development. In this technique, a broadband random signal is used as a sound

source. The normal incidence absorption coefficients and the impedance ratios of the test

materials can be measured much faster and easier compared with the first technique [72]. The

final method of measuring the sound absorption coefficient is known as,

Steady state method. This method is mostly used when the other will not work.

This particular method is described in ASTM E336-71. To measure the transmission coefficient

of the materials, a third microphone or even a second pair of microphone can be placed behind

the test sample in a second impedance tube.

Reverberant field method for measuring sound absorption is concerned with the performance

of a material exposed to a randomly incident sound wave, which technically occurs when the

material is in diffusive field [ 69]. However creation of a diffusive sound field requires a large

30

and costly reverberation room. A completely diffuse sound field can be achieved only rarely.

Moreover, an accurate value of complex impedance cannot be derived from the absorption

coefficient alone [73]. Since sound is allowed to strike the material from all directions, the

absorption coefficient determined is called random incidence sound absorption coefficient, RAC.

This method is clearly explained in ASTM C 423 – 72.

Two Microphone Impedance Tube Technique (Transfer Function Method)

The transfer function method (ASTM E 1050) covers the use of an impedance tube, with two

microphone locations and a digital frequency analysis system for the determination of normal

incidence sound absorption coefficients (NAC) and normal specific acoustic impedance ratios of

materials. This test method is similar to Test Method (ASTM C 384) in that it also uses an

impedance tube with a sound source connected to one end and the test sample mounted at the

other end. The measurement techniques for the two methods are fundamentally different,

however. First microphone tube method (standing wave method) is quite cumbersome since a

probing of the sound field has to be carried for each frequency.

The usable frequency range depends on the diameter of the tube and the spacing between the

microphone positions. An extended frequency range may be obtained by using tubes with

various diameters and microphones spacing. By this method acoustical parameters like

absorption coefficient, reflection coefficient and surface admittance for a small samples exposed

to plane waves can be determined [74]. In the fig. 6.2 (a) shows the wave propagation through

the sample and fig. 6.2(b) shows the measuring system.

(a) (b)

Fig: 6.2 (a) Sound wave propagation and (b) Measuring system configuration.

31

The major parameters to be measured are the corrected transfer function H broken down into the

real part Hr and the imaginary part Hi, the complex reflection coefficient R determined by the

real part Rr and the imaginary part Ri, and the normal incidence sound absorption coefficient �

(taking values between 0 and 1). These parameters are described below [6]:

where: H = measured transfer function;

cH = microphone calibrated factor;

j = 1− , indicating an imaginary unit in the equation;

c = speed of sound (m/s);

= density of air (kg/m3);

f = sound frequency (Hz);

k = 2�f/c (m–1); (wabe no.)

l = distance from the test specimen to the center of the nearest microphone (m);

s = center-to-center spacing between the two microphones (m);

r/c = �/[2(1 – Rr) – �], acoustic resistance ratio;

x/c = 2Ri[2(1 – Rr) – �], acoustic reactance ratio;

z/c = acoustic impedance ratio [6, 74].

32

7. Materials and methods and Experimental Results: For getting an experimental experience we have taken three types of nonwoven fabrics which

made by polypropylene. In the Department of Textile Technology, IIT Delhi, we have Normal

Impedance Tube instrument. All the results, we have got experimentally by the above mentioned

instrument. The instrument has been designed followed by ASTM C 384-98 standard. The band

frequency has taken as one-third-octave band. The lower cut-off frequency has been kept at 250

Hz. The experiment obtained up to 2000 Hz.

Details parameters of the sample has been shown in the table 7a.

Sample ID Mass (gsm) Thickness (mm) Density (gm/cc) Porosity

NPP1 378 6.24 0.06 0.93

NPP2 756 12.48 0.06 0.93

NPP3 1134 18.72 0.06 0.93

TPP1 275 0.69 0.40 0.57

TPP2 550 1.38 0.40 0.57

TPP3 825 2.07 0.40 0.57

TLPP1 82.3 0.43 0.19 0.79

TLPP2 164.6 0.86 0.19 0.79

TLPP3 246.9 1.29 0.19 0.79

Table 7(a)

NPP ---- Needlepunch Polypropylene

TPP ---- Thermalbond Polypropylene

TLPP --- Thermalbond Low gsm Polypropylene (1, 2, 3 denotes the thickness increasing)

Noise absorption coefficient has been observed in one-third octave band frequency range for all

the samples.

33

Table 7.1 shows the values of NAC with respect to Frequency (Hz) of the samples NPP1, NPP2

and NPP3.

Fig. 7.1 shows the relation between NAC and Frequency (Hz) below.

NPP1 (�) NPP2 (�) NPP3 (�)0.63 0.65 0.690.69 0.71 0.730.72 0.74 0.750.75 0.77 0.790.8 0.84 0.86

0.83 0.88 0.90.85 0.9 0.930.87 0.91 0.940.82 0.9 0.920.8 0.87 0.9

0

0.2

0.4

0.6

0.8

1

250

315

400

500

630

800

1000

1260

1600

2000

1/3 Octave band frequency (Hz)

NA

C (�

) NPP1

NPP2

NPP3

Table 7.1 Figure 7.1

Table 7.2 shows the values of NAC with respect to Frequency (Hz) of the samples TPP1, TPP2

and TPP3.

Fig. 7.2 shows the relation between NAC and Frequency (Hz) of the sample below.

TPP1 (�) TPP2 (�) TPP3 (�)0.48 0.52 0.580.5 0.55 0.620.53 0.57 0.660.58 0.62 0.690.6 0.64 0.730.64 0.68 0.770.69 0.73 0.790.77 0.79 0.830.77 0.76 0.810.74 0.76 0.77

0

0.2

0.4

0.6

0.8

1

250

315

400

500

630

800

1000

1260

1600

2000

1/3 Octave band frequency (Hz)

NA

C (�

) TPP1

TPP2

TPP3

Table 7.2 Figure 7.2

34

Table 7.3 shows the values of NAC with respect to Frequency (Hz) of the samples TLPP1,

TLPP2 and TLPP3.

Fig. 7.3 shows the relation between NAC and Frequency (Hz) of the samples below.

TLPP1 (�) TLPP2 (�) TLPP3 (�)0.46 0.49 0.540.5 0.53 0.58

0.55 0.56 0.630.58 0.6 0.660.6 0.63 0.68

0.66 0.68 0.720.69 0.7 0.750.73 0.75 0.790.76 0.77 0.790.72 0.74 0.77

0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

250

315

400

500

630

800

1000

1260

1600

2000

1/3 Octave band frequency (Hz)

NA

C (�

) TLPP1

TLPP2

TLPP3

Table 7.3 Figure 7.3 From the above all graphs, we can see that the values of � increasing with increasing the

thickness of the nonwoven samples.

The noise reduction coefficient has been shown in the table 7.4 and the fig.7.4 is showing the

tendency of NRC (%) with increasing thickness.

Sample NRC (%)NPP1 77.6NPP2 81.6NPP3 84.1TPP1 63TPP2 66.2TPP3 72.5TLPP1 62.5TLPP2 64.5TLPP3 69.1

77.681.6 84.1

6366.2

72.5

62.5 64.569.1

505560657075808590

Min Mid Max

Thickness

NR

C (%

) NPP

TPP

TLPP

Table 7.4 Figure 7.4

35

8. Aplication of sound absorptive materials: Now a days, acoustical material plays a number of important roles in acoustic engineering such

as the control of room acoustics, industrial noise control, studio acoustics and automotive

acoustics. Sound absorptive materials are generally used to counteract the undesirable effects of

sound reflection by hard, rigid and interior surfaces and thus help to reduce the reverberant noise

levels. They are used as interior lining for apartments, automotives, aircrafts, and ducts,

enclosures for noise equipments and insulations for appliances. Automotive interior noise be

undesirable for both the passenger and driver; many author have studied that the textile structures

have the potential to reduce interior noise in automobiles [75]. Sound absorptive materials may

also be used to control the response of artistic performance spaces to steady and transient sound

sources, thereby affecting the character of the aural environment, the intelligibility of

unreinforced speech and the quality of unreinforced musical sound. Combining absorptive

materials with barriers produces composite products that can be used to lag pipe or provide

absorptive curtain assemblies [30]. All noise control problem starts with the spectra of the

emitting source. Therefore, sound absorbing materials are chosen in terms of material types and

dimension, and also based on the frequency of sound to be controlled [16, 62].

Some application area:

Buildings & Construction Industrial Plants

Acoustic Ceiling Panel Automotive industries

Enclosable Noise Sources Outdoor Noise Sources

Printing Presses Public Transport

Defense Industries Aeronautical Engineering

HVAC Applications Stamping Presses

Hospital application Electronic Industries

Marine Insulation Gallery & Auditoriums etc.

36

9. Conclusion: A sound wave is an obvious parametric feature which helps us to hear something. Not only that,

sound wave is an important communicator for the daily life too. Some times the sound wave

makes us unhappy and irritated, because it’s a noisy world. Twenty-four hours a day, seven days

a week, we are exposed to sounds we do not want, need, or benefit from. There are few places on

the planet where in our daily lives we are free from unwanted sounds. We can get a pleasant

environment by controlling the noise hazards. For this purpose many people have studied how to

control the noise and make peaceful circumstances.

Lot of researchers have served the results on the sound absorption characteristics of fibrous as

well as other materials. Fibrous materials have good sound absorption characteristics. Sound

absorptive materials can be classified into three categories such as absorptive materials, Barrier

materials and damping material.

The performance of the sound absorptive materials depends on some important factors that are

fibre diameter, fiber surface area, thickness, bulk density, porosity, airflow resistivity, tortuosity

and surface impedance.

We have seen that the most important factor for sound absorption is the air flow resistivity of the

fibrous materials. Several times, researchers have found that the sound absorption coefficient (�)

increasing with increasing the airflow resistivity. Because of that, the airflow resistivity depends

on the materials porosity and bulk density. We know that, if the fibre volume fraction decreasing,

the porosity is increasing. So, porosity increasing that means the bulkiness of the materials is

increasing and airflow resistivity is decreasing. For a certain range of frequency, the sound

absorption coefficient is increasing with increasing the flow resistivity.

In this report, we have seen that the above noted factors have direct relation to the sound

absorption properties of the materials and out of that, some secondary factors also affect

indirectly. Some researchers have reported that the sound absorption coefficient is increasing

with increasing the thickness as well as bulk density and airflow resistivity.

The attenuation or dissipation of acoustic energy as a sound wave moves through a medium may

be attributed to three basic mechanisms that are, frictional losses, momentum losses and

temperature fluctuations.

37

A number of models have been established by several researchers to find out the sound

absorption characteristics of the fibrous materials. They have given some important equations

from which we can easily calculate the sound absorption coefficient of the tested materials.

Different techniques have been developed to measure the sound absorption properties of the

materials such as impedance tube methods, steady state methods and reverberant field methods

These three methods have been briefly discussed in the report.

From the experiment result and discussion, we can see that the noise absorption coefficient as

well as noise reduction coefficient is increasing with increasing thickness.

In the present society, we have seen that the sound absorptive materials have crucial demand.

Application of the sound absorbing materials to various fields is necessary. For the purpose of

the specific application of the materials, manufacturers consider the following criteria as for the

varieties of products which should be economical, durable, good aesthetic property, easy

processibility and obviously beneficial. Depending on those factors, huge applications of the

sound absorptive materials have been found in automobile industries, aeronautical industries,

building construction, hospital application, and so on.

38

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