## 2 Model Development  
### Overview  
This section presents an overview of the model to auralize accelerating passenger cars. Further, the key assumptions and motivations used for the model development are presented. In the model, each car is represented by two moving point sources. The geometrical situation is depicted in Figure 1, in which the distance of the straight driving lane to the receiver is \(D\), the emission angle \(\varphi\), the angle of inclination \(\alpha\) and the point source positions S1 and S2, respectively. Describing the kinematics of the vehicle, its speed \(v(t)\) in km/h as a function of time \(t\) (at the source) is used throughout this paper. In correspondence with the Harmonoise model [21], the point sources are vertically stacked and located at heights of 0.01 and 0.3 m above ground. By not attributing separate point sources to each vehicle axle, we limit the applicability of the model to situations with source-receiver distances clearly larger than the axial distance, while in return, saving computational costs.  
Road traffic noise is mainly composed of propulsion noise and tire noise [18; 21; 22; 23]. Both contributions differ in their relevance for the total noise, depending on the vehicle, its operating  
Figure 1: Sketch of the geometrical situation showing the two source positions S1 and S2, the inclination angle of the road \(\alpha\), the distance \(D\), the instantaneous vehicle speed \(v\), emission angle \(\varphi\), immunosuppression angle \(\theta\) and source-receiver distance \(r\).  
conditions and the pavement type. This motivates that in the presented model, the contributions of propulsion noise and tire noise are simulated individually.  
In accordance with [PERSON]'s definition of the \"principle of auralization\" [2], the presented model to auralize accelerating passenger cars comprises a separate emission, a propagation and a reproduction module. The emission module is described in Section 2.2, the propagation module in Section 2.3 and the reproduction module in Section 2.4. Figure 2 shows the block diagram of the model. The input variables describe the vehicle, driver, road surface, geometry, ground type and the weather; the input variables marked by * are time dependent.  
The emission module describes the emitted sound of an individual passenger car pass-by, _i.e._, its outside sound. In Figure 2, the emission module is edged by a gray dashed line. It contains several simulation blocks creating two separate signal paths. The upper path (red box) represents the propulsion noise and the lower path (blue box) the tire noise simulation. Key elements are two sound synthesizers that artificially generate audible emission signals for propulsion and tire noise, respectively. The synthesizer parameters can be obtained from controlled measurements, as elucidated in Section 3. Section 2.2 describes how the synthesized emission signals are attributed to the two point sources. As a proper interface to the propagation module, the point source signals are defined at a virtual reference distance of \(r_{0}=1\) m [6]. They feature time-varying sound characteristics and already include source directivity.  
For both moving source positions, S1 and S2, the sound propagation to the (static) receiver position is simulated in the propagation module. To generate the receiver signals, both corresponding source signals, \(s_{1}\) and \(s_{2}\), are filtered by a series of time-varying digital filters, as described in Section 2.3. These filters depend on the instantaneous propagation geometry, the ground type and the weather conditions (_cf._ Figure 2). Finally, in the reproduction module, the receiver signals are summed up and rendered for multi-channel reproduction using the instantaneous immission angle. Section 2.4 exemplifies a possible stereo rendering procedure.