## 4 Results and Discussion
### Wave Propagation  
The aerodynamics inside the enclosed housing for sound emission alleviation are similar to those of tunnels [47; 48]. When the train approaches the entrance of the enclosed housing for sound emission alleviation, the train head induces a compression wave, and the train rear motivates an expansion wave. Both compression and expansion waves propagate inside the housing for sound emission alleviation and reflect at both ends in sound velocity. The variation in aerodynamic pressure depends on the wave propagation. Figure 11 shows the details of the propagation of the aerodynamic pressure wave of P3 on section S9 when the train passes through. The black dotted line represents the position of the measuring point on the housing for sound emission alleviation wall, the red solid line (marked by \(T_{N}\)) is the running trajectory of the train head, the green dotted line (marked by \(T_{R}\)) is the running trajectory of the train rear, the blue solid lines (marked by \(C_{W}\)) present the propagation trajectory of the compression waves, and the blue dotted lines (marked by \(E_{W}\)) are the propagation trajectory of the expansion waves. The results show that a compression wave is generated at the instant the train head enters the housing for sound emission alleviation and then propagates inside the housing for sound emission alleviation at sound velocity. When the compression wave reaches section S9 at \(t_{1}\), the monitored aerodynamic pressure first rapidly and then steadily increases. When the train tail enters the housing for sound emission alleviation, an expansion wave is generated and propagates inside the housing for sound emission alleviation at the sound velocity. When the expansion wave reaches S9 at \(t_{2}\), the aerodynamic pressure begins to rapidly decrease. When the compression and expansion waves propagate to the exit of the housing for sound emission alleviation, they are reflected back as expansion and compression waves, respectively. At instant \(t_{3}\), the reflected expansion wave reaches S9, and the aerodynamic pressure continues to rapidly decrease. At instant \(t_{4}\), the reflected compression wave reaches S9, the aerodynamic pressure increases. When the train head passes section S9 at \(t_{5}\), the aerodynamic pressure decreases. After that, multiple compression and expansion waves are transmitted to section S6, and the pressure increases and decreases accordingly. The transmission of the aerodynamic pressure waves in the enclosed housing for sound emission alleviation is also consistent with those in tunnels, as reported by [PERSON] et al. [47]and [PERSON] et al. [48]. Figure 12 shows the pressure distribution on the wall of the housing for sound emission alleviation when \(t=6\) s. The video of the train transition with pressure shown is given in the attachment.  
Figure 11: Pressure variations of P3 on the housing for sound emission alleviation section S9 and the propagation process of the pressure waves when the train passing through the housing for sound emission alleviation: (**a**) Time history of wind pressure of P3 at S9; (**b**) Propagation process of the pressure waves (The black dotted line in (**b**) represents the test section of (**a**), the red solid line is the running trajectory of the train head, marked by \(T_{N}\); the green dotted line is the running trajectory of the train rear, marked by \(T_{R}\); the blue solid lines present the propagation trajectory of the compression waves, marked by \(C_{W}\); and the blue dotted lines are the propagation trajectory of the expansion waves, marked by \(E_{W}\)).