Sound absorption coefficient of absorbing materials may be measured according to standard test methods ASTM E 1050-08, ASTM C384-04 (2011) and ASTM C 423-09a.30,32 Normal-incidence sound absorption coefficient (NAC) may be mea­sured according to ASTM E 1050-08, the Standard Test Method for Impedance and Absorption of Acoustical Materials Using A Tube, Two Microphones and A Digital Frequency Analysis, or ASTM C384-04(2011) Standard Test Method for Impedance and Absorption of Acoustical Materials by Impedance Tube Method. Random-inci­dence sound absorption coefficient may be measured according to ASTM C 423-09a Standard Test Method for Sound Absorption and Sound Absorption Coefficients by the Reverberation Room Method.

ASTM C 423-09a includes the size and construction of the sound absorber and a reverberation room. However, the test may be costly and time consuming for an early performance estimation of noise reduction capability of composites. Further­more, it requires the test sample surface to be in massive dimensions as the mini­mum required area of the porous absorber specimen is 5.57 m2.33 While samples in small sizes are sufficient for ASTM C384-04, the testing standard requires sound absorption for each frequency to be measured separately which may take a very long time. This makes the test method ASTM E 1050-08 very feasible, taking into consideration that all data for numerous frequency points are measured simultane­ously, and small dimensions of specimens are used: a specimen diameter of 100 mm is needed for a frequency range 50-1600 Hz, whereas a diameter of 29 mm is used for 500-6400 Hz range, similar to samples shown in Fig. 5.1. Due to its practical­ity, ASTM E 1050-08 test method will be briefly described here. In order to obtain knowledge on ASTM C384-04 and ASTM C423-09a, one may refer to the men­tioned standards’ specifications.

Normal-incidence sound absorption coefficient (NAC), an, can range from 0 (no absorption) to 1 (total absorption). The formulation defines an as follows;

a.=і-И2

where ft is reflection coefficient.3 It is clear from Eq. (1) that the amount of sound absorption decreases when the reflection ratio increases. The reflection coefficient can be given as follows,

ft = . (2)

z1 + Z 0

In the expression above, z1 represents the acoustical surface impedance of the po­rous material and Z0 is the acoustical impedance of free air.3 By merging Eqs. (1) and (2), the following equation can be obtained:

Here, in the case of measurement in the impedance tube, where an is measured with the material backed by a hard wall as shown in Fig 5.2, in accordance with standard ASTM E 1050-08, the acoustical surface impedance of the porous material, z1, takes the following value:

z1 = Z0 coth (kl), (4)

where k is the wave number and l is the thickness of the material. The Eq. (4) is true, provided that the hard wall backing material has a surface impedance of z2=®. As understood from Eq. (2), the more the difference between the impedance of free air and the surface impedance of the porous material, the greater becomes the reflection coefficient.3 The schematic diagram of the impedance tube testing system is shown in Fig. 5.3 and the measurement system is shown in Fig. 5.4.

A practical tool to express noise reduction capacities of sound absorbers is the noise reduction coefficient (NRC). NRC of a material is the average of the sound absorption coefficient values at 250, 500, 1000 and 2000 Hz frequencies.32

As shown in the aforementioned expressions, acoustic impedance, z, is a very important material parameter in terms of the noise reduction performance of porous materials. Acoustical impedance is the ratio between the sound pressure, p, and the particle vibration velocity, ux, as presented by Eq. (5),10

Acoustical impedance determines a porous material’s sound absorption capabil­ity as shown in Eqs. (2) and (3). The acoustical impedance includes two compo­nents, resistance and reactance as shown in Eq. (6),

z = r + X,

where z stands for the impedance, r represents the resistance, which is a real quan­tity, and x denominates the reactance, which is an imaginary quantity.35

Among the physical parameters, flow resistance is the most critical factor de­termining the sound absorptive properties of porous materials. A good number of researchers have used air flow resistivity to model sound absorption.18,20,28,36 Even though different authors may use different denomination, terms as used in ASTM C522-03 Standard Test Method for Airflow Resistance of Acoustical Materials are adopted here and defined below accordingly.37

Flow resistance, R, in mks acoustic ohms (Pa-s-m-3), is the pressure drop across a specimen divided by the volume velocity of airflow through the specimen. Specific flow resistance, r, in mks rayls (Pa-s-m1), is the product of the flow resistance of a specimen and its area. It is equivalent to the pressure difference across the specimen divided by the linear velocity of flow measured outside the specimen. Flow resistiv­ity, r0, in mks rayl/m (Pa-s-m~2), of a homogeneous material, is the quotient of its specific flow resistance divided by its thickness. The flow resistance, R, the specific flow resistance, r, and the flow resistivity, r0 of porous materials can be given as Eqs. (7)-(9),3’37

ity (denoted by a in Delany and Bazley28, S in Mechel18) S is the area, in m2, l is the thickness, in m, of the porous material, and u is the volumetric velocity of the fluid in m3/s. Even though all these terms are concerned with steady flow and are not val­id for sound with frequencies above a few hundred Hz for some sound absorbers,13 they have been adopted by the majority of the researchers for the sake of simplicity.

The specific flow resistance is linearly related to the material thickness provided that the material is uniform. Thus, if the specific flow resistance is divided by the thickness, it will give the flow resistivity, in mks rayl/m, which is characteristic of the material independent of the thickness.29