## 2 Materials and Methods  
### Theory  
#### 2.1.1 Determination of Normal Incidence Sound Transmission Loss  
The normal incidence sound transmission loss \(nTL\) (dB) is defined as the ratio of the incident and transmitted sound power (Watts), or by means the sound transmission coefficient \(\tau\)(-) using the ITM. The transmitted and incident sound power (\(W_{t}\) and \(W_{i}\)) need to be derived from measurements in the impedance tube. Generally, the most accurate technique to determine \(nTL\) is the measurement approach based on the transfer matrix \({}^{\text{TM}}\) approach, precisely described in ASTME2611-09 [48] and ISO 10534-2 [29]. An application of the method described in the standard is given in [49]. The method requires the determination of the transfer matrix by means of a measurement of the complex sound pressure (amplitude and relative phase) at four locations, two on either side of the specimen. \[nTL=10 log_{10}\left(\frac{W_{i}}{W_{t}}\right)=10 log_{10}\left(\frac{1}{\tau} \right)=20 log_{10}\left|\frac{T_{11}+\left(\frac{T_{12}}{\rho c}\right)+\rho cT _{25}+T_{22}}{2e^{jkd}}\right| \tag{1}\]  
where \(W_{i}\), \(W_{t}\), \(\tau\), \(k_{0}\), \(c\), \(d\), and \(\rho\) are incident and transmitted sound power (Watts), transmission coefficient (-), wave number (m\({}^{-1}\)), speed of sound (m/s), diameter of the tube (m), density of the air (kg/m\({}^{3}\)) and \(T_{11}\), \(T_{12}\), \(T_{21}\), \(T_{26}\) are transfer matrix elements derived from transfer functions between sound pressure measured at the microphone positions, respectively. Usually, two different terminations (anechoic, open, minimally reflecting, etc.) are used. In specific cases, when the specimen is geometrically symmetrical and is presenting the same physical properties to the sound field on both sides, the one-load method is sufficient for use. When using this method, the effect of reflections from the termination is almost negligible. For more information about the measurement procedure, see standard ASTME2611-09 [48]. Later, a modification of the method was developed for just three microphone measurements (two in the upstream part of the impedance tube, third microphone flush mounted directly on the hard termination) [50]. Another possible method to determine \(nTL\) is based on wave decomposition (WD) theory, which deals with complex wavefields upstream and downstream of the element. The goal of the method is to decompose the wavefields in terms of forward and backward propagation waves. The method went by several modifications from three microphones (two flush mounted upstream and one downstream) developed by [PERSON] and [PERSON] [51] to four microphones (similarly mounted as in the TM approach) developed by [PERSON] and [PERSON] [52,53]. Later, the WD-TM hybrid method was developed by [PERSON] and [PERSON] [54]. They proposed a one-termination measurement approach based on a transfer matrix formulation, taking into account the reflection contribution from the end termination and the phase shift introduced by the material. The two mentioned WD methods assume a fully anechoic termination. From the WD methods, the best results might be achieved by an approach developed by [PERSON] [55], whose work was influenced by [PERSON] et al. [37], and [PERSON] et al. [56] as well. The method takes into account the complex reflection coefficient at the surface of the sample on the source side and on the termination side (\(r_{1}\) and \(r_{2}\)) as well as the complex reflection coefficient at the surface of the termination \(r_{b}\). As the reflection coefficient \(r_{2}\) can be derived just by combining two terminations measurement data, this measurement technique requires two terminations (read more about in [55]). The normal incidence transmission loss can be subsequently derived as (Equation (2)).