# The Effects of Signal System and Traffic Flow on the Sound Level
## 3 Results and Discussion
When the controlled coach was about to stop, an abrupt sound was induced due to the brake mechanism and engine system in the deceleration mode. In the acceleration duration, the peak sound level is the highest and the curve sharp is similar to the one in Figure 6b. Figure 7a,b show the average sound pressure levels \(L_{10}\) of a single controlled van plotted against the stop durations, where the \(L_{10}\) value is the level just exceeded for 10% of the time. The average sound pressure levels of the non-stop van speeds at 50 km/h are also shown on these figures (i.e., the straight lines on the figures). In general, when the stop duration goes to infinity, the average sound pressure levels converge to the corresponding sound level within the stop duration. It is because the contribution of the deceleration and acceleration to the overall sound level tends to be insignificant. For calculating the sound levels \(L_{10,DSA}\) in these figures, which are functions of the durations of the deceleration, stop, and acceleration, the following formula is used. \[L_{10,DSA}=10\log_{10}\left[\frac{10^{L_{10,D}/10}\times\Delta t_{D}+10^{L_{10,S}/10}\times\Delta t_{S}+10^{L_{10,A}/10}\times\Delta t_{A}}{\Delta t_{D}+ \Delta t_{S}+\Delta t_{A}}\right] \tag{3}\]  
where \(\Delta t_{D}\), \(\Delta t_{S}\) and \(\Delta t_{A}\) are the time durations of the deceleration, stop, and acceleration, respectively. \(L_{10,D}\), \(L_{10,S}\), and \(L_{10,A}\) are the \(L_{10}\) sound levels in the durations of the deceleration, stop, and acceleration, respectively. Figure 8a-f show the average sound pressure levels \(L_{10}\) plotted against the number of controlled vans/coaches passing through the measurement points for various speeds and stop durations. Figures 8a-c and 8d-f are the \"stop and go\" results and \"non-stop\" results, respectively. The traffic flow is 120 vans per hour. The dashed curves in Figure 8a-c denote the sound levels within the stop durations (i.e., the summation of the sound levels from those vans/coaches in the stop duration). The physical meaning of the dotted curves can be considered as \"traffic congestion\". For the \(j\)th time step, the sound levels of \(N\) vehicles in the \"stop\", \"stop and go\", and \"non-stop\" scenarios can be obtained from Equations (4)-(6), respectively. \[L_{\text{eq}(1s),S}\big{(}t_{j}\big{)}=10\log_{10}\left[10^{\frac{L_{\text{ eq}(1s),1,S}(t_{j}^{\prime})}{10}}+10^{\frac{L_{\text{eq}(1s),2S}(t_{j}^{ \prime})}{10}}+\ldots+10^{\frac{L_{\text{eq}(1s),N,S}(t_{j}^{\prime})}{10}}\right] \tag{4}\]  
\[L_{\text{eq}(1s),DSA}\big{(}t_{j}\big{)}=10\log_{10}\left[10^{\frac{L_{\text{ eq}(1s),1,DSA}(t_{j}^{\prime})}{10}}+10^{\frac{L_{\text{eq}(1s),2 DSA}(t_{j}^{ \prime})}{10}}+\ldots+10^{\frac{L_{\text{eq}(1s),N,DSA}(t_{j}^{\prime})}{10}}\right] \tag{5}\]  
\[L_{\text{eq}(1s),N\text{om}}\big{(}t_{j}\big{)}=10\log_{10}\left[10^{\frac{L_{ \text{eq}(1s),1,N\text{om}}(t_{j}^{\prime})}{10}}+10^{\frac{L_{\text{eq}(1s), 2N\text{om}}(t_{j}^{\prime})}{10}}+\ldots+10^{\frac{L_{\text{eq}(1s),N,N\text{om }}(t_{j})}{10}}\right] \tag{6}\]  
where \(N\) is the number of vehicles, \(L_{\text{eq}(1s),h,S}(t_{j})\) is the sound level of the \(h\)th vehicle at the \(j\)th time step for the stop scenario, \(L_{\text{eq}(1s),h,DSA}(t_{j})\) is the sound level of the \(h\)th vehicle at the \(j\)th time step for the deceleration, stop, and acceleration scenario (i.e., \"stop and go\" case), and \(L_{\text{eq}(1s),h,N\text{om}}(t_{j})\) is the sound level of the \(h\)th vehicle at the \(j\)th time step for the non-stop scenario. In the above calculations, distance correction must be considered in the cases of \"stop\" and \"stop and go\". For an example, when there are ten vehicles, the distances of the 3 rd to 10 th vehicles from the measurement location are longer than that of the 1 st and 2 nd vehicles. It is because Yau King Lane is a two-lane road.