Treble simulation of seat dip effects (RS7)
Treble simulation of seat dip effects (RS7)
Seat dip effects (SDE) are known to be a prominent wave phenomenon due to near-grazing incidence of sound over audience seating, showing excessive attenuation at low frequencies. The SDEs are reported since 1979, particularly in concert halls. This phenomenon is difficult to simulate with traditional geometrical acoustics (GA) software as the GA software treat the input absorption coefficients as they are valid for all incidence angles. Treble does outperform as it uses more physically correct surface impedance data at the boundaries which can correctly deal with sound attenuation for near grazing incidence cases in combination with the wave equation. One of the BRAS (Benchmark for Room Acoustical Simulation) benchmark cases is an experimental dataset of SDE, RS7. This study compares Treble simulations and BRAS.
When there are multiple rows of objects between a sound source and a receiver, sound diffracts around the objects. Particularly when the sound hits the objects at nearly grazing incidence angles almost no matter what the boundary property is, the reflection coefficient becomes -1. Therefore, this happens both in empty and occupied conditions. Because the direct path and the reflection path are almost identical, they can cancel out at a receiver location at a similar height as the source – and the receiver height and location of the stage are known as crucial factors [1-3]. One controlled experimental dataset available is BRAS RS7 as can be seen in Fig. 1. This includes 15 rows of MDF wood beams with very low-heighted source and receiver locations .
Figure 1. Seat dip effect measurement setup in RS7 from BRAS and Treble simulation snapshot .
2. Measurement setup
A Genelec 8020C sound source was used and an omni directional microphones GRAS 40AF was used in the hemi anechoic chamber RWTH Aachen (V = 296 m3) with a low frequency cutoff of 100 Hz. Each beam has a dimension of 4.14 m × 0.108 m × 0.24 m with a spacing of 2.2 – 2.44 m. In this simulation, the spacing is fixed to have 2.2 for the sake of simplicity. As this wave phenomenon can only be simulated by the wave-based methods, the pressure is calculated with a transition frequency of 1400 H. The source is modeled as omni-directional source, as the diffraction is prevailing at low frequencies where the loudspeaker typically radiates omni-directionally. The impulse response length is set to 80 ms. Two sources are located at (3.19, 2.99, 0.18) m for LS1 at (3.19, 2.99, 0.52) m for LS2. Four receivers in the Treble simulations are shown in Fig. 1. Please note that Treble only accepts two digits under the decimal point, so the effects of a slight location rounding error can be visible in simulation results too. The impulse response length was 0.07 s.
3. Simulation Results
In Fig. 2, the pressure at the four receivers are shown. Note that MP1 and MP3 has the same height, 0.34 m. Likewise, MP1 and MP3 has the same height, 0.4 m. Fairly good agreements are visible in all receiver points. Particularly the wave interference (peaks and dips) in the frequency domain is well simulated.
Figure 2. Transfer function comparison between Treble’s wave solver and measurements for BRAS RS6.
This study investigates how well Treble’s wave-based engine simulates seat dip effects. This experimental validation against BRAS RS7 demonstrates the unprecedented acoustic simulation accuracy which will be tremendously helpful to study wave phenomena in both building design and acoustic research. Some sources of the errors are uncertainties in the source and receiver locations in the measurement, an omni-directional source modeling in Treble simulation despite a directive sound source in the measurements, and spurious reflections possibly from the room surfaces in Treble, as the random incidence absorption coefficients of the boundary walls are 95%, not fully absorptive. Despite all the uncertainties, the Treble simulation results are convincing.
 Y. Ando, M. Takaishi, and K. Tada. Calculations of the sound transmission over theater seats and methods for its improvement in the low-frequency range. Journal of the Acoustical Society of America, 72(2), 443–448, (1982)
 N. Nishihara, T. Hidaka, and L.L. Beranek. Mechanism of sound absorption by seated audience in halls. Journal of the Acoustical Society of America, 110(5), 2398–2411 (2001).
 T. Lokki, A. Southern, and L. Savioja. Studies on seat dip effect with 3D FDTD Modeling, Forum Acusticum 2011, Aalborg, Denmark.
 Benchmark of Room Acoustical Simulation (BRAS) database RS7: https://depositonce.tu-berlin.de/items/38410727-febb-4769-8002-9c710ba393c4