# Experimental Validation of Treble simulations of single reflection cases

**Experimental Validation of Treble simulations of single reflection cases**

## ABSTRACT

Accurate reflection modeling in room acoustic simulation is a primary success criterion. Here, we consider three cases, rigid, absorbing, and diffuse reflection in a controlled hemi-anechoic chamber included in BRAS (Benchmark for Room Acoustical Simulation) RS1 scene. Treble outperforms the conventional GA software in simulating all types of reflections particularly at low frequencies by directly solving the wave equation.

### 1. Introduction

Acoustic predictions require accurate modeling of wave reflections off different surfaces in a three-dimensional space. An accurate simulation of each reflection is unarguably the most fundamental and crucial ingredient for precise simulation outcomes, for example, impulse responses, room acoustic parameters, auralizations. Therefore, in this report, we will present multiple comparisons of Treble’s simulation and BRAS benchmark data, RS1 (Single reflection from a finite plate).

Fig 1. Single reflection setup, Rigid surface, Absorber, Diffuser in RS1 in BRAS [1].

A Gelenec 8020C sound source was used and an omni-directional microphones GRAS 40A was used in the hemi anechoic chamber RWTH Aachen (V = 296 m3) with a low frequency cutoff of 100 Hz. The absorber panel is Rockfon Sonar G (20 mm thick) of which the flow resistivity is unknown. BRAS includes the 1/3 octave band absorption coefficients of this absorber for an incidence angle of 0. 30, and 45° [1]. The diffuser/diffusor is made of MDF, and its detailed structure is shown in Fig. 2. For the RIRs, the source and microphone points are shown in Fig. 2.

Figure 2. Source and receiver locations for RIR measurements and Treble screenshot.

In Treble, the simulation was set up as follows: transition frequency of 2000 Hz and image source order of 1 (as it is a single reflection). Treble does not accept input absorption coefficients higher than 0.95, which is based on the fact that the highest possible random incidence absorption coefficient for locally reacting surface is 0.951 for a real numbered impedance z of 1.567 [2]. This indicates that any locally reacting wall can never be totally absorbing in a diffuse sound field, and this is most likely true in most rooms. Theoretically a perfect impedance matching can occur when a panel has a surface impedance z of 1/cos(q), q being the incidence angle, which is highly unlikely anyway. The impulse response length is set to 30 ms to avoid unnecessary reflections from the other walls. For simplicity, the source is modeled as omni-directional source.

### 2. Comparison with BRAS

### 2.1. Rigid case

In this case the absorption coefficient is set to be 0.01 in Treble simulations. For the LS02 and MP04, Treble and a state-of-the-art commercial GA software are compared to the BRAS measurement in Fig. 3. Excellent agreement is shown between Treble and measurement, particularly below 2 kHz, while the conventional GA simulation fails to predict the trough locations. The magnitudes at the anti-resonances, troughs, are also quite accurate using Treble. The surface has an absorption coefficient of 0.01, which might be an underestimation of the reality because certain visco-thermal loss exists at higher frequencies, mostly visible above 3 kHz.

Figure 3. Comparison for rigid condition: Source LS2 and Microphone MP4, (a) Treble, (b) commercial GA software.

### 2.2. Absorption case

For the LS02 and MP01, Treble and a commercial GA software are compared to the BRAS measurement in Fig. 4. This is the most tricky comparison, as the true acoustic property of the absorber, Rockfon Sonar G, is unknown and not easily estimated. The creator of the BRAS dataset tried to estimate the absorption coefficients at several incidence angles, which is included in the database [1]. Treble converts the input absorption coefficient to surface impedance data for the DGFEM simulation. The converted surface impedance slightly differs depending on the incidence angle used, for example 0° or 45° angle. The result in Fig. 4(a) was obtained using the normal incidence absorption coefficient. As can be seen in Fig. 4(a) the agreement is quite satisfactory for this source-receiver pair. The other source and receiver pairs will be presented in the next section.

Figure 4. Comparison for absorption condition: Source LS2 and Microphone MP1, (a) Treble, (b) commercial GA software.

### 2.3 Diffusion case

For the LS02 and MP01, Treble and the commercial GA software are compared to the BRAS measurement for the diffuser shown in Fig. 5. The absorption coefficients for the diffuser are [0.05 0.06 0.07 0.10 0.11 0.12 0.12 0.12] for the 63-8000 Hz bands by choosing ‘Wooden chair’. It is quite evident that only the wave-based methods including Treble can do such an accurate prediction. It is well known that the common way of assigning a set of scattering coefficient on each surface in the energy-based GA simulation has no true directional information on how the diffuser scatters sound into non-specular directions and therefore fail to accurately simulate such scenarios. Therefore, the energy-based GA software just randomizes the ray directions for the scattered energy. Only solving the wave equation with the correct geometry of the room surfaces and correct boundary characteristic can truly predict the wave behavior accurately, which is shown in Fig. 5.

Figure 5. Comparison for diffuser condition: Source LS2 and Microphone MP1, (a) Treble, (b) commercial GA software.

In Fig. 6, we compared the sound pressure level difference between two reflection conditions: in Fig. 6(a) Rigid and Absorption, and in Fig. 6(b), Rigid and Diffusion. Treble shows a remarkable agreement with BRAS in several ways: accurate dip locations and a gradually increasing trend of TFRigid- TFAbs. The Pearson correlation coefficient between Treble and BRAS is 0.63, while that for the GA method is only 0.07 for the frequency range from 160 Hz to 2 kHz. The agreement for the Rigid and Diffusion condition is also remarkable with a correlation coefficient of 0.81, while the GA method shows -0.17, which means the GA simulation result tends to be opposite to the trend of the BRAS measurement.

Figure 6. The SPL difference (left) Rigid and Absorption condition, (right) Rigid and Diffusion condition. The upper figures show Treble and BRAS results and the lower figures for the other GA and BRAS results.

## 3. More Treble comparisons

In this section, we will present more comparisons to boast the capability of Treble to accurately predict the single reflection cases.

Figure 7. Comparison for Rigid condition: (a) LS1MP1, (b) LS2MP1, (c) LS3MP1.

Figure 8. Comparison for Absorption condition: (a) LS2MP1, (b) LS2MP2, (c) LS3MP3.

Figure 9. Comparison for Diffusion condition: (a) LS1MP1, (b) LS1MP2, (c) LS1MP3.

## 4. Conclusion

The Treble results in this report clearly prove that Treble outperforms the conventional commercial GA simulation in such simple acoustic environment. The GA simulation is fundamentally an approximation, which favors a quick estimation but never returns accurate simulations. On the other hand, Treble as a hybrid wave-based and geometrical acoustics method successfully overcomes the problems of all the energy-based approximate calculations and will definitely be acousticians’ favorite simulation tool.

## References

[1] Benchmark of Room Acoustical Simulation (BRAS) database RS5: https://depositonce.tu-berlin.de/bitstreams/ccce535a-c508-4046-8748-4458b8e73d13/download

[2] H. Kuttruff, “Room Acoustics” 6th edition, Taylor and Francis, 2017.