## 4 Results and Discussion
### Model Validation  
The sound absorption simulation of the 5 \(\upmu\)m diameter fiber porous material was conducted at three densities: 80 kg/m\({}^{3}\), 100 kg/m\({}^{3}\), and 120 kg/m\({}^{3}\). The results were then compared with the actual measurements, as shown in Figures 9-11. The experimental and simulated data for the single-fiber porous materials at these three densities showed a high degree of consistency, with errors maintained at about 5% (4.95%, 5.26%, and 5.88%, respectively). These results confirm the effectiveness of the three-parameter model in predicting the acoustic performance of single-fiber porous materials. However, for fiber-particle composite materials, the three-parameter model exhibits some deviation. At a density of 80 kg/m\({}^{3}\), the composite material shows the maximum error of 12.81% when 30% zeolite particles are added. At densities of 100 kg/m\({}^{3}\) and 120 kg/m\({}^{3}\), the maximum errors occur when the zeolite addition is 20%, with errors of 12.43% and 12.08%, respectively. Figure 9: Comparison between the measured and simulated results of the sound absorption coefficient of porous materials with different zeolite additions at 80 kg/m\({}^{3}\): (**a**) zeolite: 0%, (**b**) zeolite: 10%, (**c**) zeolite: 20%, (**d**) zeolite: 30%. with a small amount of zeolite, the experimental values are higher than the simulated ones. This is because high-frequency sound waves are primarily absorbed at the surface of the material, while low-frequency sound waves are absorbed deeper inside the material [49]. When a large amount of zeolite is added, the particles block the pores of the porous material, restricting the penetration and absorption of sound waves, leading to the low-frequency experimental sound absorption coefficients being lower than the simulated values. Conversely, when a small amount of zeolite is added, it does not obstruct sound wave penetration and creates a significant pressure diffusion effect, and the actual sound absorption effect will be higher than the simulation value. Thus, these are two distinct effects, resulting in larger errors in the low-frequency range compared to the high-frequency range. Additionally, the discrepancy may also be attributed to the unique layered structure of the composite porous material. As observed in the experiments, the composite material consists of multiple layers of ultrafine glass fibers and zeolite particles stacked together. During the stacking process, the uneven surfaces of the glass fiber layers and zeolite particle layers can introduce small air layers between the fiber layers, as illustrated in Figure 12a. Additionally, the presence of inorganic particles attached to the fiber layers further complicates the interface. Due to the reflection of sound waves at the boundary between the air layer and the sound-absorbing material layer, the sound wave is reduced by the interference of the wave in the air layer [50]. On a microscopic level, this layered structure can be conceptualized as numerous \"three-layer\" units composed of a \"loose (fiber)\(-\)dense (fiber + zeolite particles)\(-\)loose (fiber)\" structure. Additionally, Figure 12b illustrates the sound absorption mechanism of the composite material. The left side presents an overall schematic of sound wave propagation within the composite material, while the right side provides a detailed mechanism of horizontal sound wave propagation. In the diagram, red lines represent incident sound waves, and blue lines denote reflected sound waves. When sound waves penetrate the composite material, a portion of the sound energy is converted into kinetic and thermal energy, while the remaining portion continues to diffuse and propagate. The presence of air gaps between adjacent layers and the dissimilarity of materials in different layers create impedance mismatches at the interfaces, increasing the probability of sound wave reflection at these boundaries [51].