## 2 Materials and Methods
### Analytical Model for Infinite and Finite Homogeneous Orthotropic Panel
For frequencies containing the lowest panel resonance frequency and for \(f<f_{c1}/2\), Equation (1) may be approximated by assuming the panel behaves as a limp mass and wave impedance \(Z_{orth}\) can be written:  
\[f=\frac{\omega}{2\pi} \tag{2}\]4  
Thanks to this, Equation (11) becomes:  
\[f=\frac{\omega}{2\pi} \tag{2}\]5  
For frequencies between \(f_{c1}\) and \(f_{c2}\), provided that \(\eta=0\), [PERSON] also gives an approximation to Equation (11):  
\[f=\frac{\omega}{2\pi} \tag{2}\]6  
Additionally, also for \(f>f_{c2}\), the diffuse field transmission coefficient can be calculated from the equation:  
\[f=\frac{\omega}{2\pi} \tag{2}\]7  
The transmission loss of panel, \(TL\), is defined in terms of the transmission coefficient-\(\tau_{d}\):  
\[f=\frac{\omega}{2\pi} \tag{2}\]8  
Transmission loss is commonly observed by testing in a reverberation room. The transmission loss is usually measured by placing the panel in a window between two adjacent reverberant rooms. Noise is introduced into one of the rooms (the source room), and part of the sound energy is transmitted through the test panel into the second room (receiver room). So, during measurements, panels are not of an infinite extent. It is possible to perform numerical integration of Equation (11) for various ranges of frequency, and transmission loss can then be calculated by substituting \(\tau_{d}\) in Equation (16). Panels are not of infinite extent, and results obtained by these equations do not agree well with results measured in the laboratory. [PERSON] [38] showed that this limiting angle depends on the size of the panel and that good comparisons between prediction and measurement transmission loss can be obtained if the upper limit of integration of Equation (11) is changed so that the integration does not include angles of \(\theta\) between some limiting angle and \(90^{\circ}\). This allows the use of some approximations [33], such as in our studies. For a corrugated panel, as an orthotropic panel, with critical frequencies \(f_{c1}\) and \(f_{c2}\), the prediction scheme as a function of frequency could be taken into account, which should give reasonably good agreement with the experiment, according to [PERSON]'s studies. At frequency \(f=f_{c1}/2\), it may be assumed that the panel behaves as a limp mass and transmission loss \(TL\) can be calculated as:  
\[f=\frac{\omega}{2\pi} \tag{2}\]9  
For \(f_{c1}<f<f_{c2}/2\), the following approximation can be used:  
\[f_{c1}=\frac{c^{2}}{2\pi}\sqrt{\frac{m}{B_{x}}} \tag{3}\]0For \(f=2f_{c2}\), transmission loss TL is calculated from:  
\[f_{c1}=\frac{c^{2}}{2\pi}\sqrt{\frac{m}{B_{x}}} \tag{3}\]1  
Above \(2f_{c2}\), the TL is given by:  
\[f_{c1}=\frac{c^{2}}{2\pi}\sqrt{\frac{m}{B_{x}}} \tag{3}\]2  
The transmission loss between \(0.5f_{c1}\) and \(f_{c1}\) and between \(0.5f_{c2}\) and \(2f_{c2}\) is approximated by connecting points corresponding to the frequency with a straight line [33]. Another way to determine the acoustical parameters of panels is a computer simulation. Acoustic computer simulation is widely used in building acoustics. They can predict the acoustic performance of buildings or construction materials before they are built, which is helpful in modifying the acoustic design if necessary. The finite element method (FEM) can be applied to large and complex structures with various boundary conditions. It is the most popular method among numerical techniques for panels. FEM is proposed by various researchers for the structural analysis of corrugated plates of uniform thickness and equivalent rigidities [39; 40; 41; 42]. These techniques apply if the dimensions of the whole corrugated panel are much larger than the period of the corrugations. Additionally, when there is no access to transmission loss test measurements, numerical simulations of plates or panels can be an important alternative. Modelling transmission loss was performed using deterministic methods such as Finite Element (FEM) or Boundary Element (BEM) for low and middle frequencies.