## 4 Conclusions  
The results of the studies described in this article present a new approach to cleaning exhaust gases from internal combustion engines based on the use of ultrasonic transmitters in a car muffler. The authors analyzed the theoretical aspects of the effect of ultrasound on gases, taking into account the work of [PERSON], [PERSON], and other scientists. However, the existing theoretical provisions are limited to the consideration of the Brownian motion of particles in a gas and do not take into account the influence of forces and pressure during ultrasonic exposure on the gas flow in the car muffler. In addition to Brownian motion, hydrodynamic particle motion is also observed in the muffler, and turbulence may occur in the gas flow. As a result, the proposed theories cannot fully capture the physical nature of the processes that take place inside the muffler. This study involved a mathematical analysis of the passage of gas particles in a muffler through an ultrasonic field, creating a physical picture of the process taking into account the forces acting on the particles during the movement. The results of the analysis of the equation of motion of a particle in an ultrasonic field justified the need for an experimental study and allowed us to identify independent experimental parameters: the angular velocity of rotation of the engine crankshaft and the frequency of oscillation of the ultrasonic wave. To evaluate the efficiency of gas cleaning in an ultrasonic field, the authors proposed an optimality criterion based on the ratio of exhaust smoke before and after ultrasonic exposure. Figure 12: Change in the ratio of the gas smoke content from the values of the ratio of the ultrasound frequency to the angular speed of the engine crankshaft, \(f/\omega\). The results of the experiment showed that the introduction of an ultrasonic transmitter into the muffler reduced the smoke content of the gas, increased the oxygen content, and reduced the amount of carbon dioxide in the exhaust gases. With an increase in the ratio between the ultrasonic frequency and the angular velocity of the engine crankshaft (\(f\)/\(\omega\)), the smoke content of the gas also decreased. In particular, at the maximum values of ultrasonic frequency and angular velocity of the engine crankshaft selected in the experimental studies, the minimum value of the ratio of gas smoke indicators was achieved, and the degree of purification was 10-13%. Such results correspond to the condition of optimal operation of the ultrasonic muffler, where the ratio of gas to smoke values should tend to a minimum. These results confirm the potential of using ultrasound as a method for cleaning exhaust gases and underline the need for further research in this area. The perspective of this research is focused on the possibility of creating a system for regulating the parameter \(f\)/\(\omega\) while maintaining its necessary parameters. This allows to minimize the values of \(D_{2}\)/\(D_{1}\). Thus, this study represents an important contribution to the development of new methods of exhaust gas purification, and its results may contribute to a more efficient and environmentally friendly operation of vehicles. Conceptualization, A.K. ([PERSON]), B.S., M.B. and A.K. ([PERSON]); methodology, A.K. ([PERSON]), M.B., B.S. and A.K. ([PERSON]); software, S.N. ; validation, S.N. ; formal analysis, S.N. ; investigation, A.K. ([PERSON]), B.S., M.B. and A.K. ([PERSON]); resources, A.K. ([PERSON]) and B.S. ; data curation, A.K. ([PERSON]); writing--original draft preparation, A.K. ([PERSON]), B.S., M.B. and A.K. ([PERSON]); writing--review and editing, S.N., B.S. and A.K. ([PERSON]); visualization, A.K. ([PERSON]); supervision, A.K. ([PERSON]) and M.B. ; project administration, B.S. ; funding acquisition, B.S. All authors have read and agreed to the published version of the manuscript. This research has been funded by the Science Committee of the Ministry of Science and Higher Education of the Republic of Kazakhstan, Grant No.