## 1 Introduction  
The investigation of tire acoustic cavity resonance noise (TACRN) has absorbed the attention of the industry and academia since its contribution to the interior noise of a car. When a car is running, the interaction between the road surface and tire treated with pattern generates the excitation with wide frequency bandwidth enough to cover the first-order natural frequency of the tire acoustic cavity, thus resulting in TACRN [1; 2; 3; 4]. Grasping the characteristics of TACRN is a key step in investigating the attenuating strategy. To this aim, many researchers have performed a series of investigations, especially in revealing the mechanism of TACRN, predicting its modal characteristics, and analyzing the influences of load and velocity [5; 6; 7]. [PERSON] et al. [8] first clarified the modal characteristics of tire cavity resonance by means of the finite element simulation and road test and put forward the calculation formula of the cavity resonance frequency. [PERSON] [9] developed a closed-form solution to predict the resonance frequencies of the deflected tire and performed experimental verification. It was also shown that the cavity resonance of the deflected tire generated forces acting at the spindle simultaneously along vertical and fore-aft directions with slightly different frequencies. [PERSON] and [PERSON] et al. [10; 11] included the effect of the tire cavity resonance in a more refined structural-acoustic tire model, and a finite cylindrical cavity with rigid boundary conditions was employed. The model could help to predict the effect of the cavity resonance on the spindle forces as well as identify the potential noise control design. [PERSON] and [PERSON] et al. [12; 13; 14] paid attention to the influences of the coupling of tire, cavity, and rim on the TACRN and verified the simulation models by using different analysis approaches. [PERSON] and [PERSON] [15; 16] showed a numerical model of the tire cavity with passive resonators to reduce the TACRN, and the larger the number of resonators was, the better the ability to attenuate the cavity noise over a wider frequency range was. [PERSON] et al. [17; 18; 19] researched the mechanism and characteristics of the frequency split phenomenon and novel modal of TACRN from different aspects, and the obtained function could help to determine the frequency variation range under different conditions, and the theoretical calculation results were verified by the experiment and simulation. The above works showed that the researchers regarded the acoustic wave in the tire cavity as a plane wave, and then analyzed the characteristics of tire acoustic cavity resonance. According to the existing literature, it can be concluded that, in the past modeling and analysis, TACRN was straightforwardly assumed to be the plane wave or was qualitatively described as a plane wave without analyzing the feasibility. However, there exist strict conditions for the acoustic wave propagating in the pipeline to act as a plane wave, and TACRN is a typical acoustic wave propagating in the pipeline. Therefore, it is necessary to investigate TACRN's evolution law and the conditions of TACRN being regarded as a plane wave. However, to the authors' knowledge, there is not yet a paper that completely describes the conditions for an acoustic wave in a tire cavity to evolve into a plane wave. Aiming at this problem, in this paper, firstly, the tire acoustic cavity is simplified under the premise of maintaining its essential characteristics, and its acoustic model is established. Then, the propagation and attenuation characteristics of an acoustic wave in the cyclic tire cavity are quantitatively researched based on acoustic waveguide theory, and the existence range of a higher-order wave (non-plane wave) is analyzed. Next, the conditions of evolving into a plane wave and the frequency range of a plane wave are verified and revealed through the finite element method.