# Design and Testing of a Gasoline Engine Muffler Based on the Principle of Split-Stream Rushing
## 1 Introduction
When the frequency of the noise is lower than the first higher-order mode excitation frequency of the muffler (i.e., the plane wave cutoff frequency), the sound wave propagates inside the muffler in the form of a plane wave. Therefore, plane wave theory can be used to calculate the acoustic properties of the muffler. The application of the transfer matrix method provides a brand-new solution for the calculation of the acoustic performance of mufflers. [PERSON] et al. conducted a systematic and comprehensive study in 1954 and discussed the acoustic characteristics of mufflers with different structures under the condition of no airflow, including a single-stage expansion chamber muffler, a multi-stage expansion chamber muffler, and a side-branch resonator [4]. However, plane wave theory still has some limitations in analyzing practical problems. Plane wave theory can be applied when the noise frequency is lower than the first higher-order mode excitation frequency of the muffler. Under these conditions, plane wave theory can be used to calculate the acoustic performance of the muffler. However, in practice, the noise frequency is often very high, exceeding the plane wave cutoff frequency, resulting in higher-order modal waves inside the muffler. At this time, the sound field inside the muffler is three-dimensional, so plane wave theory cannot be applied to predict the internal sound field of the muffler. Faced with such a problem, a solution is quickly found. The three-dimensional analytical method is an effective means of establishing a three-dimensional sound field simulation for a muffler with regular geometry. In order to calculate and analyze the multidimensional wave effect, many scholars have proposed different muffler design methods, including the modal expansion method, the matching point method, and the mode matching method. These methods are widely used in muffler design. In the actual situation, the structure inside the muffler is complex and variable and not symmetrical, so scholars proposed the use of the finite element method, a numerical calculation method, to calculate and analyze those mufflers with complex structural forms. In the 1970s, [PERSON] et al. introduced the finite element method for the first time in the muffler acoustic characteristic analysis and calculation. With the gradual improvement of the acoustic calculation theory, more and more scholars invested in research on muffler acoustic performance [5]. [PERSON] et al. pointed out that the acoustic performance of a reactive muffler is greatly affected by the number of holes in the inlet and outlet pipes, as well as their positions at the target frequency [6]. [PERSON] et al. addressed the issue of difficult suppression of low-frequency noise in pipelines and designed a composite broadband muffler by using a combination of a pair of Helmholtz resonance cavity array acoustic panels and a perforated pipe muffler, achieving low-frequency broadband high muffling [7]. Scholars have studied how to make the muffler's acoustic performance reach an ideal state while also noticing a performance index that is equally important for mufflers: exhaust back pressure. Exhaust back pressure refers to the change in the air pressure at the exhaust valve before and after the engine is connected to the exhaust system. [PERSON] used CFD software to find the location of the exhaust back pressure in the exhaust system, providing the basis for the subsequent optimization of the exhaust back pressure of diesel engines [8]. [PERSON] used GT-power to optimize the internal structure of the muffler of a formula car. The internal structure of the muffler of a formula racing car was optimized by using GT-power, reducing the exhaust noise by 20% while preserving the dynamics of the car [9]. [PERSON] et al. used CATIA to create a three-dimensional model of the muffler, simulated its Transmission Loss by using Virtual. Lab 12 acoustic simulation software, and finally improved the muffler to meet the requirements of exhaust back pressure [10].