# Design and Testing of a Gasoline Engine Muffler Based on the Principle of Split-Stream Rushing
## 2 Materials and Methods
### Evaluation Index  
#### 2.1.1 Acoustic Performance Evaluation Index  
In this paper, the main evaluation indexes of acoustic performance used in the design of split-stream rushing muffler are Transmission Loss and insertion loss.  
1. Transmission Loss  
Transmission Loss is defined as the difference between the incident sound power level at the inlet of the muffler and the transmitted sound power level at the outlet when there is no reflective end at the outlet and when there is a one-dimensional plane wave in the channel [15], expressed as  
\[\mathrm{TL}=\mathrm{L}_{W_{i}}-\mathrm{L}_{W_{t}}=10\mathrm{log}_{10}(W_{i}/W _{t}) \tag{1}\]  
where \(W_{i}\) and \(W_{t}\) are the incident sound power at the muffler inlet and the transmitted sound power at the outlet, respectively. Since the Transmission Loss is only related to the muffler itself, independent of the impedance of the sound source and the radiation impedance of the orifice, it is widely used for simulation in the early stage of muffler design. However, when conducting muffler Transmission Loss experiments, it is necessary to accurately measure the incident sound pressure and transmitted sound pressure inside the pipe, but these two values are often difficult to measure. Therefore, it is typically not possible to measure the muffler's Transmission Loss during testing. Moreover, the Transmission Loss is more suited for evaluating of the acoustic performance of an ideal muffler under ideal conditions and is not practical compared to the insertion loss of a real vehicle.  
2. Insertion loss  
The insertion loss is the difference between the sound power level of the noise radiated from the orifice before and after the installation of the muffler. When the sound field distribution is kept approximately constant during the test, the insertion loss is the difference between the sound pressure level before and after the installation of the muffler at a given measurement point [16].  
\[\mathrm{IL}=\mathrm{L}\mathrm{P}^{\prime}-\mathrm{L}\mathrm{p}=20\mathrm{lg} \,|\,\mathrm{P}^{\prime}/\mathrm{P}\,| \tag{2}\]  
Given that the acoustic radiation impedance at the outlet of the piping system remains essentially unchanged before and after the installation of the muffler, the insertion loss can accordingly be expressed as  
\[\mathrm{IL}=20\mathrm{lg}\,|\,\mathrm{P}^{\prime}{}_{2}/\mathrm{P}{}_{2}\,| \tag{3}\]  
where \(\mathrm{P}^{\prime}{}_{2}\) and \(\mathrm{P}{}_{2}\) are the sound pressure at the outlet of the piping system before and after the installation of the muffler, respectively. The noise source, the muffler, the pipeline, the pipe outlet, and the surrounding environment will affect the insertion loss to different degrees, so the insertion loss is not only an attribute of the muffler alone but also an attribute of the whole system. Therefore, the insertion loss can often be a more realistic response to the muffling performance of the muffler. However, because the muffler needs to simulate the evaluation indexes of the muffler in the pre-design process, the insertion loss is obviously not an evaluation index that can be well simulated, so the insertion loss is not taken as the simulation object in the simulation stage. Mostly, the muffler insertion loss test is carried out in the final physical experiment stage.