# Mechanism Analysis of the Influence of Seat Attributes on the Seat Dip Effect in Music Halls
## 3 Results and Discussion
### Possible Mechanism  
To clarify the influence mechanism of the seat attributes on the SDE mentioned above, two sets of detailed investigations on sound wave behavior between the seats were conducted in simulations on the possible mechanism related to the SDE. For the first investigation set, the color map results of the SPL and sound intensity (SI) distribution at different frequencies inside the rigid seat gaps are presented in Figure 6a-c where \(h\) = 0.8 m, \(w\) = 1.1 m and in Figure 6d-f where \(h\) = 1.1 m, \(w\) = 0.8 m. The color represents the SPL, and the arrows represent the SI magnitude and direction. In Figure 6a-f, the first phenomenon is that the SI magnitudes gradually decrease from the outside to the inside of the seat gaps, and the SI directions rotate clockwise between the seats and create energy flow vortexes showing the presence of standing waves, as reported by [PERSON] [1]. The lowest SPL position always appears at the gap center with the height of \(\lambda\)/4, which is the center point of the energy flow vortex shown in Figure 6a-e with heights of 0.81 m, 0.65 m, and 0.57 m at the frequencies of 105 Hz, 130 Hz, 150 Hz, respectively. It is worth noting that Figure 6f features the two lowest SPL positions at the gap center with heights of 0.35 m and 1.06 m, which are equal to the \(\lambda\)/4 and 3\(\lambda\)/4 of the investigated frequency, 240 Hz, respectively. This phenomenon of the lowest SPL positions inside the seat gaps located at the gap center, with the height ((2k + 1) \(\lambda\))/4 (k = 0, 1, 2...), shows the first influence mechanism on the SDE from seat height and spacing. The second phenomenon is that, when the energy flow vortexes appear near the top surface of the seats, for example the vortexes near the slats' upper ends, as shown in Figure 6a,b,f, the grazing incident waves are observed to be \"diffused\" by the energy flow vortexes and a continuous attenuation can be created around the top surface of the seats due to this complex interference. This can be another influence mechanism on the SDE from seat height and spacing. These phenomena come not only from the interference between the grazing direct sound and the verticallyreflected sound waves inside the seat gaps, but also from those between the oblique sound incidence and horizontal sound reflections inside the seat gaps. For the second investigation set, the color map results of the SPL and SI distribution at the corresponding dip frequencies are presented in Figure 6g-I, where \(\alpha_{\rm c}=0.0\), \(h=1.1\) m and \(w=0.8\) m for the influence of the seat back absorption and Figure 6j-I, where \(\alpha_{\rm b}=0.0\), \(h=1.1\) m, and \(w=0.8\) m for the influence of the seat cushion absorption. The absorptive seat boundaries (backs or cushions) are marked with thick red lines, while the rigid ones are marked with thick grey lines. It is shown that seat absorption has a clear guiding effect on the SI directions, where sound energy flows are observed to be guided by the absorption to become horizontal into seat backs, in Figure 6g-I, or to become vertical into seat cushions, in Figure 6j-I. Additionally, inside the seat gaps, the horizontal reflections are distinctly reduced by the seat back absorption, as shown in Figure 6h-i, and vertical reflections are distinctly reduced by the seat cushion absorption, as shown in Figure 6k-I. The wave guiding effect and standing wave suppression from the seat absorption remarkably level out the energy distribution and weaken the energy flow vortexes due to the complex interference inside the aforementioned seat gaps, and then reasonably suppress the SDE. This could be the influence mechanism on the SDE from the seat back or cushion absorption.