# Acoustical Properties of Fiberglass Blankets Impregnated with Silica Aerogel
## 4 Results and Discussion
### Acoustical Properties  
The acoustical properties were measured at the University of Sheffield in a 10 mm impedance tube [25]. Five specimens were cut from different areas on a sample of each type of fibrous blanket and their properties were measured. The repeatability of each measurement was found within \(\pm\)2.9% for the absorption coefficient and \(\pm\)5.8% for the reflection coefficient. Figure 8 shows a comparison between the measured absorption coefficients for the five samples. Figure 9 presents a comparison between the measured and predicted real and imaginary parts of the complex reflection coefficients for these five materials. Figure 8: An example of the measured sound absorption coefficient of a 8–9 mm thick hard-backed layer of the five fibrous blankets with a progressive increase in the aerogel filling ratio. Figure 7: SEM images taken at different magnifications (3000\(\times\) **(a)**, 800\(\times\) **(b)** and 200\(\times\) **(c)**) showing the fiberglass blanket structure with an aerogel filling ratio of 100%. Figure 9: Examples of the measured (marker) and predicted (solid lines) complex reflection coefficient data for fiberglass blanket without any aerogel (**top**), 50% aerogel impregnated blanket (**middle**) and 100% aerogel impregnated blanket (**bottom**). The results presented in Figure 8 suggest that there is a progressive increase in the absorption coefficient as the aerogel impregnation increases from 0 to 50%. When the aerogel filling ratio reaches 75% this increase becomes less pronounced. Increasing the filling ratio beyond 75% reduces the absorption coefficient significantly. This reduction makes sense because it is likely associated with a densely packed inter-fibrous space, which becomes almost full with aerogel (see Figures 6 and 7), causing a considerable reduction in the pore size (see Table 1) in a relatively thin material layer. For the filling ratios of 75% and above the characteristic impedance (see Figure 9) and attenuation of sound in a layer with such small pores becomes very high, limiting the value of the absorption coefficient [27]. The absorption coefficient of this relatively thin fibrous blanket with 50-75% filling ratios is still relatively high (30-70%) particularly above 1000 Hz (see references [4,13]). This level of absorption has a practical value in applications related to engineering noise control. An obvious question here is: _What happens to the fiberglass pore properties when the percentage of aerogel powder impregnating the blanket increases?_ In order to answer this question we attempted to fit the mathematical model [28] to the complex acoustic reflection coefficient data measured in the impedance tube. We used the optimization procedure described in reference [30] to invert the three parameters of the best fit. This procedure has been used extensively by many researchers (see [27] for a review of parameter inversion methods). Figure 9 shows three examples of this fit for fiberglass blankets with aerogel filling ratios of 0, 50 and 100%. Table 1 presents a summary of the mean values of the three non-acoustical parameters in the adopted theoretical model [28], which were inverted from its fit to the measured data for the five filling ratios. This table also provides the porosity values calculated from the material density data, mean layer thickness measured directly and root mean square error (RMS) calculated between the predicted and measured reflection coefficient spectra. The superscript \({}^{(i)}\), which appears with a non-acoustic parameter in this table, means that the values of this parameter were inverted rather than measured directly. The results shown in Figure 9 and the parameter values listed in Table 1 suggest that the model generally provides a very close fit to the data (an RMS error better than 2.5%), particularly when the filling ratio is equal to or below 50%. The agreement between the predicted and measured reflection coefficient spectra reduces slightly with the increased filling ratio.