## 3 Results
### Uncertainties in the Measurements and Calculations  
A fundamental question was which statistical characteristics approximate the expected value and uncertainty of \(L_{f}\) and the total combined uncertainty of \(\Delta L_{f}\).  
We applied the Shapiro-Wilk test to check whether the \(L_{f}\) values were normally distributed for each FFP and frequency combination [15]. The normal distribution hypothesis could not be rejected in 164 out of 192 cases, i.e., for 85% of the datasets in the centre frequency range 100-20 kHz at the significance level \(p<\) 0.05. \(L_{f}\) in 86 out of 96 datasets for the \(f\) range from 800 Hz to 10 kHz, i.e., 89%, showed normal distribution. However, we decided to reject the normal distribution model for the sake of consistency in calculations. We noticed that the \(L_{f}\) values were normally distributed in only five out of 24 frequency bands for all measurement series, with and without FFPs. Consequently, the attenuations \(\Delta L_{f}\) and their uncertainties estimated from the arithmetic means, and variances could be compared for five bands only, these with centre frequencies of 315, 630, 2000, 5000, and 12,500 Hz. Thus, we used medians and ranges rather than arithmetic means and standard deviations as characteristics of the variables' distributions. In the vast majority of cases, the medians and means: arithmetic, geometric and harmonic, were equal within the limits of \(\pm\)0.1 dB. The difference never exceeded the limits for the class 1 sound meter. The latter is \(\pm\)1.1 dB for \(f\) = 1 kHz and is higher for other frequencies [13].  
The ranges of \(L_{f}\) (no FFP) values were close to the measurement uncertainty limits for the class 1 sound meter. The largest range of \(L_{f}\) (no FFP) was 2.0 dB for the 1/3 octave  
Figure 2: Attenuation of sound in 1/3 octave-wide bands by Folded FFPs. For a detailed description, see the Figure 1 caption.  
wide band with the centre frequency of 250 Hz, while that for \(L_{\rm 1 kHz}\) (no FFP) was 1.5 dB. Contrary to the \(L_{f}\) ranges for the uncovered TalkBox speaker, those of the \(L_{f}\) (with the FFP) significantly exceeded the sound meter uncertainty limits.  
According to the classical calculus of errors, the maximum error of \(\Delta L_{f}\) is the sum of the maximum errors of \(L_{f}\) (no FFP) and \(L_{f}\) (with the FFP) in Equation (1):  
\[\varepsilon\Big{(}\Delta L_{f}\Big{)}=\varepsilon\Big{[}L_{f}(\text{no FFP}) \Big{]}+\varepsilon\Big{[}L_{f}(\text{with the FFP})\Big{]} \tag{2}\]  
The measurement errors seldom add up in this most unfavourable manner [16]. Moreover, the errors are symmetric in this approach. In our measurements, the median value usually did not lie in the middle of the minimum-maximum value range. Thus, the asymmetric errors approach seemed a better choice for uncertainty estimation. The lower and upper limits of the \(\Delta L_{f}\) value, \((\Delta L_{f})_{\rm low}\) and \((\Delta L_{f})_{\rm upp}\), were calculated from Equation (1) in the following way:  
\[\Big{(}\Delta L_{f}\Big{)}_{\rm low}=\min\Big{[}L_{f}(\text{no FFP})\Big{]}- \max\Big{[}L_{f}(\text{with the FFP})\Big{]} \tag{3}\]  
and  
\[\Big{(}\Delta L_{f}\Big{)}_{\rm upp}=\max\Big{[}L_{f}(\text{no FFP})\Big{]}- \min\Big{[}L_{f}(\text{with the FFP})\Big{]} \tag{4}\]  
where \"min\" and \"max\" denote the minimum and maximum values in the series of ten measured sound pressure levels in the 1/3 octave-wide band.