# Experimental Analysis and Simulation of a Porous Absorbing Layer for Noise Barriers
## 2 Materials and Methods
### Experimental Methods
#### 2.2.2 Measurement of the Sound Absorption Coefficient  
To obtain the sound absorption coefficient under normal incidence conditions, laboratory tests were performed on a circular impedance tube with 100 mm internal diameter (Figure 6). The test methodology is described in ISO 10534-2 [17], which is based on the transfer function between two microphones.  
The impedance tube used has a cut-off frequency of about 1600 Hz. The sound pressure was measured using two G.R.A.S. Sound and Vibration (Denmark) 46 AE 1/2\"  
Figure 5: Experimental determination of macroscopic parameters of the porous concrete: (**a**) Schematic diagram of the setup and instrumentation used for the tortuosity laboratory tests; (**b**) setup for the determination of the airflow resistivity, following the ISO 9053-2 [40].  
Figure 6: Impedance tube with 100 mm internal diameter.  
CCP Free Field microphones, a NI USB-4431 dynamic signal acquisition (DSA) device, from National Instruments (USA), connected to a PC laptop and the registered pressure data has been recorded and processed in MATLAB 2016 implemented codes. A random excitation, provided by a loudspeaker in one end of the impedance tube, was generated from the NI USB-4431 DSA.  
The ratio between the reflected pressure (\(p_{r}\)) and the incident pressure (\(p_{i}\)) is the reflection factor that is given by:  
\[r=\frac{p_{r}}{p_{i}}. \tag{4}\]  
On the other hand, the sound absorption coefficient can be achieved with the following expression:  
\[\alpha=1-|r|^{2}. \tag{5}\]  
where \(r\) is the reflection coefficient. This experimental test also provides an important parameter that characterizes the acoustic absorbing material, the surface impedance, given by:  
\[Z_{sf}=\rho_{0}c_{0}\frac{(1+r)}{(1-r)}. \tag{6}\]  
where \(Z_{0}=\rho_{0}c_{0}\) is the characteristic air impedance.  
To evaluate the sound absorption in diffuse field conditions, experimental tests were performed on a reverberant room. This test methodology is proposed in ISO 354 [18]. The diffuse incidence absorption coefficient measurement procedure consists of making reverberation time (RT) measurements of the reverberant room under two distinct conditions: firstly, with the reverberant room empty and, afterwards, with the sample to be characterized placed directly over the floor of the reverberation room, with the perimeter edges of the test specimen sealed with a reflective frame of gypsum boards and reflective adhesive tape sealing the joints along the perimeter (see Figure 7). In accordance with the above-mentioned standard, based on [PERSON]'s formula, the equivalent absorption area of the porous concrete sample can be achieved with:  
\[A_{T}=A_{2}-A_{1}=55.3V\left(\frac{1}{c_{2}RT_{2}}-\frac{1}{c_{1}RT_{1}}\right) -4V(m_{2}-m_{1}), \tag{7}\]  
in which \(V\) corresponds to the volume of the empty reverberant room, \(c_{1}\) corresponds to the propagation speed of sound in air at temperature \(t_{1}\) with the empty room, \(m_{1}\) corresponds to the attenuation coefficient due to the presence of air with the empty room, \(RT_{1}\) corresponds to the reverberation time of the empty room, and \(c_{2}\) corresponds to the sound propagation velocity in the air at temperature \(t_{2}\) with the sample placed in the room, \(m_{2}\) corresponds to the attenuation coefficient due to the presence of air with the sample in the room, and \(RT_{2}\) corresponds to the reverberation time with the sample in the reverberant room. The sound pressure was measured using two G.R.A.S. Sound and Vibration 46 AE 1/2\" CCP Free Field microphones, a Symphonic acquisition system, from 01 dB, with dBBati32 controlling software.  
Figure 7: Experimental setup according to ISO 354 [18] with the porous concrete sample placed on the floor of the reverberant room (type A mounting): (**a**–**c**) different source and microphone positions are observed.