# Mechanism Analysis of the Influence of Seat Attributes on the Seat Dip Effect in Music Halls
## 1 Introduction  
In music halls, when sound passes at a near grazing incidence over the seats, there is a phenomenon of excessive attenuation in the low-frequency band. Different from the sound absorption attenuation that usually occurs at high frequencies caused by sound being absorbed by the audience and the surfaces of the seats, this attenuation phenomenon, known as the seat dip effect (SDE), occurs at about 100 Hz and seems typical in music halls despite the difference made to the sound by the audience. The effect was first discovered by two studies through investigations in concert halls and scale models [1; 2], early in 1964. Subsequently, in situ or scale-model measurements [1; 2; 3; 4; 5; 6; 7], and theoretical calculations [8] were extensively conducted to analyze the SDE. It was shown that the SDE caused the excessive attenuation of sound at low frequencies within the hall, which significantly affected spatial impression [9], clarity [3], and timbre [4; 10] by affecting the early reflection of the sound, and people's perception of bass frequencies was significantly stronger in concert halls with higher SDE attenuation frequencies [11]. Recently, computer simulations were applied to study the SDE with the wave-based geometrical acoustics method, the finite element method (FEM), the boundary element method (BEM) [12] and the finite-difference time-domain method [13]. The parameters with a possible influence on the SDE were investigated, such as the floor inclination [5], sound incident angle [4; 14], and ceiling height [4; 7]. Based on these investigations, some guidelines were proposed to reduce the SDE, such as: (1) increasing the ceiling reflection or the side reflections [15; 16]; (2) installing ground sound absorbers between the seat rows [3; 8]; and (3) sloping the floor or the stage [5; 14], etc. However, for the SDE suppression, choosing the appropriate seat attributes of height, spacing and absorption is a more implementable way than raising the floor slope oradding reflectors, and seat attribute adjustment can be implemented easily in renovations which affect the hall construction. Regarding the influence of seat attributes on the SDE and possible mechanism, early studies [1; 2] showed that the frequency of the maximum attenuation mainly depended on the height of the seat. Later, [PERSON]'s measurements [17] investigated the influence on the SDE from the seat underpass and observed that the dip frequency increased for higher source positions when the height of the seat underpass decreased. Measurements and practical calculations suggested that the SDE was affected by the diffraction on the seat top [3] and by the reflected sound on the auditorium seats [14]. [PERSON] and [PERSON] [12] compared the SDE attenuation with different seat absorptions and seat underpass shapes using the BEM simulation and a scale model and reported that changing the seat absorption had an audible influence on reducing the SDE in concert halls. [PERSON] et al. [18] conducted scale-model experiments to study the effect of the seat underpass and floor inclination on the SDE, and found that the dip frequency depended on the seat back height and on the obstruction degree of the seat underpass. However, little investigation and discussion on the possible mechanism was conducted in [12; 18]. [PERSON] [7] investigated the SDE phenomena via scale model measurements and derived a simple analytical model for attempting to explain the SDE mechanism. In his study, the SDE attenuations with different seat back absorptions were investigated and it was found that the seat backs affected the SDE attenuation and dip frequency shift. However, it was difficult for [PERSON] to further explore the mechanism due to the limited simulation techniques of that time and only assumption was made that the SDE was highly related to the interference between a direct wave and reflected waves from the seats.