Treble simulation of diffraction (RS6)
Treble simulation of diffraction (RS6)
Diffraction is a prominent low frequency phenomenon that is known to be difficult to simulate with traditional geometrical acoustics (GA) software even with some compensations. Treble outperforms the conventional GA software in simulating diffraction from a large barrier by directly solving the wave equation as shown in the BRAS (Benchmark for Room Acoustical Simulation) RS5 scene. This study compares Treble simulations and BRAS for the RS6 scene called finite diffracting body.
When there is an impenetrable obstacle between a sound source and a receiver, sound diffracts around the obstacle. Examples include diffraction around a noise barrier outdoors and diffraction around furniture typically in room conditions. Diffraction is an important phenomenon in room acoustics that traditional energy-based geometrical acoustics methods cannot simulate properly. There are some ways to add diffraction in geometrical acoustics, such geometrical theory of diffraction  and analytical secondary source modeling  etc. Treble’s wave-based solver, discontinuous Galerkin method, solves the wave equation directly, and therefore the Treble’s solution must be superior to the energy-based geometrical method. In this application note, a diffraction scenario is simulated in Treble, which is RS6 case in BRAS database , as shown in Fig. 1.
Figure 1. Diffraction measurement setup in RS6 from BRAS and Treble simulation snapshot .
2. Comparison with BRAS
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. The box has a dimension of 4.14 m × 0.72 m × 0.72 m. One the day of measurement, the temperature was 20.3 °C and the humidity was 40.3 %.
In Treble, the simulation was done up to 2000 Hz (as transition frequency) only by the wave-based solver. The source is modeled as omni-directional source, as the diffraction prevails at low frequencies where the loudspeaker typically radiates omni-directionally. The impulse response length is set to 40 ms. The source is located (2.49, 2.99, 0.8) m, which corresponds to LS3 in the BRAS database. Two receivers in the Treble simulations are (8.51, 2.99, 0.4) m and (8.51, 2.99, 0.8) m, which are MP2 and MP3 in the BRAS RS6 dataset, respectively. Please note that Treble only accepts two digits under the decimal point, so a slight rounding error is observed in the source and receiver location and simulation results too. Treble currently recommends the source position at least 50 cm from the surfaces and receiver positions at least 15 cm from the surfaces.
Figure 2. Transfer function comparison between Treble’s wave solver and measurements for BRAS RS6.
It is clear that Treble shows excellent agreement in the trough locations, which actually shows destructive interference due to diffracted wave components from the edges.
This study investigates how sound diffracts around a finite obstacle using Treble simulation, which is experimentally validated against BRAS RS6 data. It is clear that Treble simulation matches well with the measurement data thanks to its accurate acoustic solver. Some sources of the errors are uncertainties in the source and receiver locations in the measurement, an omni-directional source modeling in Treble simulation, and spurious reflection 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, which is a strong point for simulating room acoustics at low frequencies.
 JB Keller, “Geometrical theory of diffraction,” Journal of the Optical Society of America, 52 (2), 116-130 (1962).  UP Svensson, RI Fred, J Vanderkooy, “An analytic secondary source model of edge diffraction impulse responses,” Journal of the Acoustical Society of America 106 (5), 2331-2344 (1999).  Benchmark of Room Acoustical Simulation (BRAS) database RS6: https://depositonce.tu-berlin.de/items/38410727-febb-4769-8002-9c710ba393c4