# A Metawindow with Optimised Acoustic and
## 3 Results
### Acoustic Performance Based on Experimental Measurement
#### 3.1.2 AMW Unit Performance on the Lower Frequency Range (500-1000 Hz)  
It is also important to notice that in the frequency range below 380 Hz and between 700 and 900 Hz, the _IL_ related to Point B goes below zero. Since the sound wave that passes through the AMW unit is then refracted through the four openings on the window frame, such a configuration might originate new noise sources characterised by a different mode that varies in the space. Therefore, the _IL_ dips measured in Points B and C are probably due to a superposition of the sound wave's low-frequency component when it exits from the four openings on the window frame. For this reason, the measurements for Point B show there is such a low dip between 700 and 900 Hz, whereas the graph shows that for Point A (_IL_(A)) the dip is much higher (_IL_(A - B) = 10.6 dB). Generally, excluding the frequency range of 700-900 Hz for _IL_(B), the sound wave pressure level on a broad frequency range from 300 to 5000 Hz is shown to be significantly affected by the AMW unit system. 3.1.3. Determination of the Coefficient of Variation for the Validation of the Numerical Method through the Experimental Results  
The numerical method is validated through experimental results in terms of _IL_ and about each measurement point. _IL_ slopes are observed with their characterising peaks and dips in terms of the coefficient of variation (\(CV\)) according to the frequency range:  
\[CV=\frac{RMS_{1}}{RMS_{2}}\times 100\ (\%) \tag{2}\]  
where the root mean square (\(RMS_{1-2}\)) expresses the measure of the magnitude of the _IL_ values and is used to determine the standard deviation and mean between the numerical and experimental results:  
\[RMS_{1}=\sqrt{\frac{\sum_{i=1}^{N}\left(IL_{Num,i}-IL_{Exp,j}\right)^{2}}{N}} \tag{3}\]  
where:  
* \(RMS_{1}=RMS\) to determine the standard deviation;  
Figure 3: (**a**) Experimental analysis results in terms of _IL_ related to measurement points A, B, and C. (**b**) Comparison of _IL_ results related to the numerical and experimental studies on Points A and B. Six peaks are distributed along the overall range, where the first is between 300 and 1000 Hz, the second between 1000 and 2000 Hz, the third between 2000 and 3000 Hz, the fourth between 3000 and 4000 Hz, and the fifth and sixth between 4000 and 5000 Hz. \(IL_{Num,i}=IL\) calculated from the numerical method (dB);
* \(IL_{Exp,i}=IL\) calculated from the experimental method (dB);
* \(N=\) sample size. \[RMS_{2}=\sqrt{\frac{\sum_{i=1}^{N}IL_{Exp,i}{}^{2}}{N}} \tag{4}\]  
where:  
* \(RMS_{2}=RMS\) to determine the mean. The \(CV\) is the standard deviation ratio to the mean and shows the variability of the population's mean. Therefore, the higher the \(CV\), the greater the dispersion of the \(RMS\). Figure 3b compares the \(IL\) results at Points A and B from the experimental measurement and the numerical simulation. In the graphs, six peaks distributed along the frequency range are possibly highlighted (see Figure 3b). The simulation curve captures the main variation trend and the occurrence of \(IL\) peaks well. The \(CV\), as defined in Equation (2), is used to evaluate the correspondence between the experiment and the simulation. Table 1 shows the values of \(CV\) in the subdivided frequency ranges. A generally good agreement between the numerical and experimental results can be found within the broad frequency range: the \(CV\) is always below 40%, excluding \(CV\) (B) at low frequencies (300-1000 Hz). The discrepancies between the experimental and simulation curves can possibly be attributed to a few reasons. First, the simulation's frequency step size is much wider than that used in the experiment, mainly limited by the heavy computation cost. Therefore, the simulation is used to capture the \(IL\)'s magnitude and its variation behaviour while neglecting the frequency fluctuations. Second, the experimental setup slightly differs from the numerical model, mainly in the sound source condition and the \(IL\) evaluation points.