## 3 Results and Discussion
### Impact Noise-Tapping Machine
When considering the range of 250-3150 Hz, we can also easily derive a regressive equation (Equation (10)):  
\[\Delta\mathrm{L}^{\prime}_{\mathrm{n,w,ceiling}}=-0.028\ (\mathrm{f})+23.8\ ( \mathrm{dB}) \tag{10}\]  
where f is the frequency [Hz]. The results could be fitted, with a regression coefficient of R\({}^{2}\) = 0.89. By means of this equation, it could be possible to estimate the effect of this kind of suspended ceiling on a generic CLT floor of 20 cm thickness. Moving onto configuration 3 (only floating floor and bare CLT floor), it could be acknowledged that a similar reduction is proposed, compared to configuration 2. Here, low frequencies (100-200 Hz) are reduced more efficiently, as well as high frequencies (1600-4000 Hz). However, this technology could not work properly, because its performance requires a heavy mass as bare floor. In this case, a cross laminated plate could not represent this element, because of its lightweight structure. When applying Equation (7) to configuration 3, a different resulting trend is produced. In Figure 11, the frequency tendencies of the two impact noise reductions are depicted. Clearly, [PERSON]'s model cannot be applied to this kind of wooden partitions, since it fails by a large amount. The main reason is that [PERSON]'s model considers the bare floor as completely rigid, featuring an ideally infinite mass in comparison to the floating floor. In the case of CLT floors, this does not happen. Accordingly, the density of a CLT floor is 90 kg/m\({}^{2}\), very similar to the floating floor. It is evident that the bare timber floor cannot be considered neither more rigid nor more massive than the floating floor, thus significantly affecting the application of [PERSON]'s model. Figure 10: Impact sound pressure level for CLT floors (configurations 1, 2, 3, and 4). Source: tapping machine. When investigating the frequency influence on the measured noise reduction index reported in Figure 11, in the range 250-3150 Hz, a relation can be found, as expressed in Equation (11), with a regression coefficient of R\({}^{2}\) = 0.70. However, a poor influence of frequency on impact noise reduction is highlighted:  
\[\Delta\mathrm{L}^{\prime}_{\mathrm{n,w,floating,CLT\ model}}\ =-0.012\ \mathrm{f}+22.9\ ( \mathrm{dB}) \tag{11}\]  
when combining the two technologies in the bare floor (configuration 4), a significant reduction is verified, in comparison to configuration 1 (bare CLT floor) and to both configuration 2 and 3. Anyway, when combining Equations (10) and (11), the obtained result is not reliable (Figure 12). Figure 11: Comparison between Cremer’s and measured \(\Delta\mathrm{L}^{\prime}_{\mathrm{n,w}}\) for configuration 3. The retrieved equation from measured values is reported below, with a regression coefficient of R\({}^{2}\) = 0.81 (Equation (12)). \[\Delta\Gamma^{\prime}_{\text{m,w,overall}}\ =-1.9\ \text{f}+40.1\ (\text{dB}) \tag{12}\]  
Here, we can see that frequency affects more significantly impact sound reduction, in comparison to configuration 2 and 3. It is thus evident that we have to avoid the combination of the two equations related to single actions, as the merging would lead to a significant underestimation of the final results.