## 2 Methods
### Noise Spectra of Different Vehicle Types and Speeds  
To analyze the frequency characteristics of traffic noise of different types of vehicle with various speed, the 1/3 rd octave band spectrum data of vehicles were recorded, including 34 frequencies from 10 Hz to 20,000 Hz. To facilitate the analysis of the frequency characteristics, the following ranges are defined: frequencies from 10 Hz to 315 Hz are low frequency; 400 Hz to 800 Hz are medium-low frequency; 1000 Hz to 2500 Hz are medium-high frequency; 3150 Hz to 20,000 Hz are high frequency. To analyses the frequency characteristics of traffic noise and exclude the effect of SPL, the noise energy percentage of the 1/3 rd octave band spectrum was calculated [34], as given by the following formulas (Equations (1)-(3)):  
\[E(i,j)=10^{0.1*L(i,j)} \tag{1}\]  
\[E^{\prime}(i,j)=\frac{E(i,j)}{\sum\limits_{j}E(i,j)} \tag{2}\]  
\[E_{S}(j)=\frac{\sum\limits_{i}E^{\prime}(i,j)}{i} \tag{3}\]  
where \(i\) is the number of vehicles, \(j\) is the number of frequencies; \(L(i,j)\) is the SPL (dB), \(E(i,j)\) is the relative value of noise energy (dimensionless quantities), \(E^{\prime}(i,j)\) is the noise energy percentage (%), and \(E_{S}(j)\) is the mean percentage of noise energy (%).  
From the equations, the SPL of each frequency of each vehicle is transformed to the noise energy percentage of each frequency. Figure 2 depicts the average noise energy percentage versus frequency for each type of vehicle with different speeds.  
\begin{table}
\begin{tabular}{c c c c} \hline \hline
**Speed** & **Light Car** & **Middle Car** & **Heavy Car** \\ \hline
[0, 40) km/h & 39 & 23 & 41 \\
[40, 50) km/h & 186 & 48 & 80 \\
[50, 60) km/h & 317 & 57 & 55 \\
[60, 70) km/h & 222 & 38 & 36 \\
[70, 80) km/h & 134 & & \\ \(\geq\)80 km/h & 75 & & \\ \hline \hline \end{tabular}
\end{table}
Table 1: Distribution of the samples of vehicle noise spectra.  
Figure 1: Locations of the Measurement Spots.  
As shown in Figure 2, the noise energy percentage of the different speeds of three types of vehicles were performed with the 1/3 rd octave band spectrum frequencies in the range of 10-20,000 Hz. The following points can be made:  
1. For a light vehicle, the noise energy is concentrated in the range of 500-2500 Hz, with peak frequency at approximately 1250 Hz. For a middle vehicle, the noise energy is concentrated in the range of 315-2500 Hz, with peak frequency at approximately 1600 Hz. For a heavy vehicle, the noise energy is concentrated in the range of 315-2500 Hz, with peak frequency at approximately 500 Hz.  
Figure 2: Noise energy percentage with the 1/3 rd octave band spectrum frequencies at different speeds of three types of vehicles. (**a**) light vehicles; (**b**) middle vehicles; (**c**) heavy vehicles.  
* Speed will affect the SPL of a vehicle and the frequency characteristics of a vehicle. Noise spectra exhibit a trend of concentrating as the speed increase. Take the light vehicle case as an example, the noise energy percentage at the primary frequency range of 1000 Hz to 2500 Hz increases with speed, whereas the percentage of insignificant frequencies, such as low and medium-low frequencies, decrease with speeds. In addition, the main frequencies increase as the speed grows, especially for a light vehicle.
* The noise frequencies of the heavy vehicles are mainly medium-low frequency and medium-high frequency, which is quite different from the noise frequencies of light and middle vehicles, as their frequencies are mainly medium-high frequency.
* The emission noise of a vehicle can be divided into engine noise and tire/asphalt noise. Most of the light vehicles have gasoline engines. The contribution of engine noise is far less than the tire/asphalt noise. The proportion of diesel engines is high when for middle vehicles and heavy vehicles. The noise caused by diesel engine represents a large proportion, leading to a bi-modal trend in the noise spectra, which is in agreement with the rules presented by previous studies [34; 35].