## 2 Acoustic Performance Evaluation Indicators for an Expandable Duct Silencing System
### Experimental Verification of Transmission Loss of Mufflers  
Experiments on the expansion chamber duct muffler's noise reduction performance were carried out in order to confirm the correctness of the simulation results. In Figure 8, the experimental concept is displayed. First, to reduce the impact of background noise, the noise frequency range is adjusted using computer software and signal-to-noise ratio testing is carried out. The speaker is then controlled to produce noise signals upstream of the impedance tube by adjusting the amplitude of the noise signal by employing a power amplifier. Ultimately, the transmission loss test results were computed by gathering the incident and reflected sound wave signals at the front and back ends of the expansion chamber duct muffler using four pre-calibrated microphones.  
Figure 7: Sound pressure level cloud diagram for expansion chamber mufflers.  
In this test, the air duct cavity section was set to a square of \(5\text{ cm}\ \times\ 5\text{ cm}\), the expansion chamber cavity section was set to a square of \(11.2\text{ cm}\ \times\ 11.2\text{ cm}\), the expansion ratio \(m\) was 4.8, and the cavity length \(L\) was 2 cm in order to better adapt the expansion chamber muffler to the square impedance tube. The testing apparatus is depicted in Figure 9.  
The test findings are displayed in Figure 10, where it is evident that the results of the acoustic finite element simulation computation are compatible with the trend of the transmission loss test value of the expansion chamber duct muffler with frequency variation. The transmission loss test's peak value is lower than the simulation's result and its peak frequency moves toward lower frequencies as a result. This is the consequence of the test sample being constructed from iron sheets and cardboard that have been joined. The expansion chamber's radial mode is not well aroused due to manufacturing flaws and the construction itself and the modal frequency also exhibits some degree of fluctuation. The test findings' noise reduction features, on the other hand, deviate considerably from the one-dimensional transmission loss calculation model and are generally in line with the simulation results. This shows that the one-dimensional transmission loss calculation model is only appropriate in cases with longer cavity lengths and verifies the viability of the acoustic finite element simulation analysis approach.  
This suggests that the acoustic finite element model of the air conditioning duct muffler may be more accurately computed and fitted to the real world using the COMSOL Multiphysics acoustic module. Furthermore, studies have shown that the expansion chamber air duct muffler has a good noise reduction effect. Additionally, while maintaining the expansion chamber's cross-sectional area, a smaller chamber length L can enhance the noise reduction performance of the expansion chamber noise reduction unit.  
Figure 8: Impedance tube transmission loss testing apparatus schematic diagram.  
Figure 9: Physical diagram of impedance tube transmission loss testing equipment.