## 3 Acoustic Analysis of Dual Cavity Composite Duct Mufflers
### The Influence of Parameters on the Acoustic Performance of Dual Cavity Composite Silencers  
Dual chamber composite duct mufflers provide more steady broadband noise reduction properties as compared to dual chamber mufflers and dual chamber sound absorption mufflers. Based on the dual chamber composite air duct muffler model in Figure 11, examine the effects of the expansion ratio \(m_{1}\) and the length of the expansion chamber \(L_{1}\) of the first expansion chamber silencing unit on the dual chamber composite air duct muffler in order to determine the relationship between structural parameters and acoustic characteristics of the muffler. The expansion ratio \(m_{1}\) should not be chosen too greatly because of the coordination between the air conditioning duct and other parts. The expansion ratios of 1.62, 1.94, and 2.29 were obtained by increasing the thickness by 4 cm, 6 cm, and 8 cm based on the initial air duct size. It is evident from the data displayed in Figure 18a that the expansion ratio significantly affects the muffler's acoustic performance. The peak frequency range of the dual cavity composite muffler changes toward lower frequencies as the expansion ratio \(m_{1}\) develops and the peak noise reduction in the muffler increases in addition. This is because the expansion chamber's radial mode is activated, beginning at around 1000 Hz. The frequency corresponding to the radial mode is also lower when the length of the expansion chamber \(L_{1}\) is constant because the bigger the expansion ratio \(m_{1}\), the smaller the ratio between the length of the expansion chamber \(L_{1}\) and the cross-sectional diameter \(D_{1}\). Figure 18: Transmission loss curves for various dual cavity composite muffler parameters. (**a**) Different expansion ratios \(m_{1}\); (**b**) Different cavity lengths \(L_{1}\); (**c**) Different expansion ratios \(m_{2}\); (**d**) Different cavity lengths \(L_{2}\); (**e**) Different spacing \(L_{0}\). The acoustic properties of a dual chamber muffler with chamber lengths of 2.5 cm, 5 cm, and 7.5 cm and the first expansion chamber silencing unit are displayed in Figure 18b. The figure illustrates how the length of the cavity affects the peak frequency band of the dual cavity composite air duct muffler; however, it has very little effect on the noise reduction amplitude. The expansion ratio \(m_{2}\) and the chamber length \(L_{2}\) were modified and the transmission loss was computed, taking into consideration the impact of the structural characteristics of the second expansion chamber absorption unit on the acoustic performance of the muffler. Figure 18c,d displays the outcomes. The figure illustrates how the sound reduction amplitude of the dual chamber composite muffler is somewhat influenced by the expansion ratio of the sound-absorbing expansion chamber sound-absorbing unit \(m_{2}\). The cavity is filled with more sound-absorbing material as the expansion ratio rises, which enhances the sound absorption effect in the mid-to-high frequency range. Conversely, the dual cavity composite muffler's noise reduction amplitude is mostly unaffected by the cavity length \(L_{2}\) but is affected in a specific frequency region. Finally, an investigation is conducted into how the muffler's acoustic performance is affected by the distance \(L_{0}\) between its two expansion chamber silencing components. The dual chamber composite duct muffler's transmission loss is computed by considering \(L_{0}\) to be 5 cm, 10 cm, and 15 cm, according to Figure 18e. The diagram's results indicate that the peak noise reduction in the muffler is somewhat influenced by the distance \(L_{0}\) between the two expansion cavity silencing units. The peak noise reduction rises with an increase in \(L_{0}\). To sum up, the total noise reduction performance of a dual chamber composite air duct muffler is influenced to variable degrees by its characteristics.