## 3 Acoustic Analysis of Dual Cavity Composite Duct Mufflers  
### Acoustic Finite Element Model of Dual Cavity Composite Duct Mufflers  
As illustrated in Figure 11, the dual chamber composite air duct muffler is composed of two expansion chamber silencing devices. One of the expansion chamber sound-absorbing units, which has a cavity length of \(L_{1}\) of 5 cm and a cross-sectional area of \(S_{1}\), is vacant. The other expansion chamber has a cavity length of \(L_{2}\) of 10 cm, a cross-sectional area of \(S_{2}\), and is filled with porous material that absorbs sound. The cross-sectional area of the duct \(S_{0}\) stays constant at 286 cm\({}^{2}\), the dual chamber composite muffler's total length L stays constant at 25 cm, the cross-sectional area of the two expansion chambers \(S_{1}=S_{2}=656\) cm\({}^{2}\), and the expansion ratio \(m_{1}=m_{2}=2.29\). These values are used to compare the acoustic performance of the expansion chamber duct muffler. The acoustic properties of the expansion chamber air duct muffler may be efficiently enhanced by packing the chamber with porous materials that absorb sound waves. Sound waves may be absorbed by porous materials that transform them into thermal energy [33; 34]. This lowers noise levels by minimizing sound waves' reflection and propagation. The goal of choosing \(L_{1}<L_{2}\) is to obtain greater attenuation peaks by making use of a short cavity expansion chamber's non-planar wave attenuation properties. The transmission loss results of an acoustic finite element simulation for a dual cavity composite duct muffler operating in the frequency range of 0 Hz to 1500 Hz are displayed in Figure 12.  
Figure 11: Composite double-champered air duct muffler. Figure 10: Test data for the expansion chamber muffler’s transmission loss. The dual chamber composite air duct muffler has a more notable noise reduction impact than the expansion chamber muffler under the same expansion ratio (\(m\)), as can be seen in the picture. At least a 5 dB increase in transmission loss occurs in the frequency range of 650 Hz to 1250 Hz. Its noise reduction impact may be enhanced by at least 10 dB, particularly in the frequency range of 850 Hz to 1000 Hz and 1125 Hz to 1200 Hz. Furthermore, a peak in noise reduction was noted at around 1175 Hz. Further investigation into the dual chamber composite duct muffler's acoustic performance will be carried out, taking into consideration the sound pressure level cloud map:  
The expansion chamber sound-absorbing device, in the absence of any additional materials, has good resistance qualities based on the sound pressure level cloud map in Figure 13. The expansion chamber has a rather high and focused sound pressure level in the frequency range of 650 Hz to 1175 Hz, which suggests that there are a lot of reflected sound waves occurring at these frequencies. The distribution of sound pressure levels becomes more complicated as the frequency increases. Non-planar waves began to form around 1125 Hz and at 1175 Hz a distinct longitudinal distribution and the phenomenon of sound pressure backflow were seen. Furthermore, the sound-absorbing equipment with an expansion chamber and other sound-absorbing materials has strong resistance features. The sound pressure level close to the sound-absorbing material is comparatively low, with a good sound absorption effect in the 850 Hz to 1500 Hz range, as can be seen from the sound pressure level cloud map. The distribution of sound pressure levels throughout the whole muffler is quite consistent, as can be seen from the sound pressure level cloud map at 1375 Hz, and the twin chamber muffler's sound reduction effect exhibits a local valley around this frequency. In terms of noise reduction, the twin-chamber composite air duct muffler possesses resistance and structural features. Within the broad frequency range of 650 Hz to 1500 Hz, it has a good noise reduction impact but as frequency increases, so does transmission loss.