# Mechanism Analysis of the Influence of Seat Attributes on the Seat Dip Effect in Music Halls
## 3 Results and Discussion
### Seat Absorption  
In the numerical cases above, the SDE phenomenon is investigated with rigid seats and a rigid floor. It is interesting to investigate what occurs when the seats become sound absorbing. [PERSON] and [PERSON] (2012) conducted a rough observation on the SDE with several seat absorption coefficients but did not analyze in detail the corresponding strength and characteristic changes of the SDE. In this section, numerical cases are carried out for the SDE with a different seat back absorption coefficient \(\alpha_{\text{b}}\) and seat cushion absorption coefficient \(\alpha_{\text{c}}\) where \(h=1.1\) m and \(w=0.8\) m. The corresponding \(RL\) spectrum results are presented in Figure 4c,d, respectively. It can be observed that, through increasing the seat back or cushion absorption coefficient from \(0.0\) to \(1.0\), the dip minimum \(RL_{0}\) gradually changes from \(-46\) dB to around \(-23\) dB, demonstrating that the SDE attenuation is remarkably weakened by the seat absorption. It is also shown that, the dip frequency \(f_{0}\) may increase to higher frequencies with a higher seat absorption, especially at the seat back. A similar phenomenon was observed by [PERSON] (2017), whose complete mechanism is unclear yet and can be related to sound distribution around the vertical slats that are assumed as simplified geometry of seat backs (2017). For a direct visual inspection on the influence of seat absorption, the color maps of the SPL spatial distribution at the corresponding dip frequencies of the SDE with different \(\alpha_{\text{b}}\) or \(\alpha_{\text{c}}\), as shown in Figure 4c,d, are presented in Figure 5. Figure 5a,b show the situations of seat back absorption and seat cushion absorption, respectively. In the color maps, the color represents the SPL, and the streamline is derived from the gradient of the calculated sound intensity. As shown in Figure 5, there is no SDE when no seat is in the room. When the rigid seats are set, there is a distinct area of the SDE concentrated at almost the entire surface of the seat tops, with a continuous attenuation of sound energy, and the SDE area becomes larger at seat locations farther away from the source. In Figure 5a, as \(\alpha_{\text{b}}\) increases, the concentration strength of the sound energy attenuation is gradually weakened and the area of the sound energy attenuation gradually shifts backwards from the front seats. This shows that the diminishing tendency of the SDE by seat absorption is from the front seats to the rear seats. Therefore, the SDE attenuation investigated at the R4-R6 receiving points (whose positions are marked by black stars in each color map) decreases as \(\alpha_{\text{b}}\) increases from \(0.0\) to \(0.9\), as shown in Figure 4c. Meanwhile, the streamlines in Figure 5a also gradually extend into the seat gaps, showing that more sound energy flows into the seating area with a higher seat absorption. When \(\alpha_{\text{b}}=1.0\), the SDE attenuation around the surface of the seat tops becomes much weaker in comparison to the situation with no seats. Figure 5b presents a similar diminishing tendency of the SDE by seat cushion absorption, but the corresponding SDE reduction is observed to not be as distinct as the reduction by the seat back absorption shown in Figure 5a. Through a cross comparison between the results in Figure 5a,b, it is shown that the appropriate sound absorption treatment of the seat back or cushion can play a certain role in suppressing the SDE in music halls, and the seat back absorption is more effective than the seat cushion absorption. From other extensive simulation cases, when \(h\) is not larger than \(w\), similar results (not presented here for conciseness) also show a greater beneficial effect on the SDE from the seat back absorption rather than from the seat cushion absorption, and this observation is consistent with discussion presented in Ref. [12].