# Binaural Auralization of Room Acoustics with a Highly Scalable Wave-Based Acoustics Simulation
## 4 Binaural Room-Acoustics Auralization in a Large-Scale Auditorium
### Objective Analysis of Auditorium Room Acoustics
Figure 13a-d show four room-acoustics parameters, the reverberation time (T30), the early decay time (EDT), the A-weighted relative sound pressure level (SPL (A)), and the rapid speech transmission index (RASTI) at six receivers R1\(\sim\)R6 for Cond. 1 and Cond. 2. Those parameters were evaluated using ODEON 16 room-acoustics simulation software with computed RIRs with the present wave-based solver. The reverberation times and EDT have averaged values greater than 500 Hz and 1 kHz. The reverberation times of both conditions show large differences, with spatially averaged values of 1.52 s for Cond. 1 and 0.93 s for Cond. 2. Their relative differences at each receiver are 35-45%. A large difference in EDT between both conditions is also notable. The spatially averaged EDT values are 0.96 and 0.64 in Cond. 1 and Cond. 2. The relative differences between Cond. 1 and Cond. 2 at the same receivers of 20-52% are much larger than the just notable difference (JND) of 5% [38]. From these results, we can infer that the auditory impression of auralized sounds, which comes from the additional side wall absorbers, shows a clear difference in reverberance. In addition, SPL(A) results show that SPL(A) becomes smaller for the receiver positions going in the back of the auditorium. For Cond. 1 and Cond. 2, SPL(A)s at R5 are \(-4.1\) dB and \(-5.1\) dB compared to those at R1. In addition, an SPL(A) comparison at the same receivers shows that SPL(A)s in Cond. 1 present more than 1 dB larger values than those of Cond. 2. The maximum difference is 2.3 dB at R6. A comparison of RASTI between both conditions shows that RASTI values in Cond. 2 take larger values more than  
Figure 10: Simulated FOA signals at R3 in Cond. 1: (**a**) \(A_{0,0}\); (**b**) \(A_{1,-1}\); (**c**) \(A_{1,0}\); and (**d**) \(A_{1,1}\). JND value of speech transmission index of 0.03 [39] at all receivers than those of Cond. 1. The RASTI values are 54-58% in Cond. 1 and 56-65% in Cond. 2. We also expect distinct differences of speech clarity in auralized speech sounds between the two conditions. Figure 11: Simulated FOA signals at R3 in Cond. 2: (**a**) \(A_{0,0}\); (**b**) \(A_{1,-1}\); (**c**) \(A_{1,0}\); and (**d**) \(A_{1,1}\). Figure 12: Directivity patterns in early and late times on a horizontal plane against azimuth \(\phi\) with the following absorption and receiver conditions: (**a**) Cond. 1 and R3; (**b**) Cond. 1 and R4; (**c**) Cond. 2 and R3; and (**d**) Cond. 2 and R4. Figure 14 presents a comparison of frequency characteristics of spatially averaged reverberation time and EDT with the Eyring-Knudsen formula. The error bars in numerical results show their standard deviations. The Eyring-Knudsen formula values and T30 values differ except for Cond. 1 at 125 Hz, indicating low diffusivity of sound fields. In Cond. 1, T30 becomes larger with frequencies above 500 Hz, whereas the average absorption coefficient decreases with frequency. The frequency characteristic of Cond. 2's T30 shows the same tendency as the average absorption coefficient because of cancellation of the flutter echo with the additional absorber. Moreover, EDT values agree with the Eyring-Knudsen formula, which is better than T30 except for Cond. 1 at 125 Hz. The result indicates that the wave-based room-acoustics solver accurately models frequency-dependent absorption characteristics of boundary surfaces. We present examples for BRIRs calculated with FOA signals and HRIR at R3 and R4 for Cond. 1 in Figure 15. The BRIRs are calculated after rotating FOA signals so that the front of a listener is in \(\phi=180^{\circ}\). Consequently, direct sound arrives from the front at R3, whereas it comes from the left obliquely forward at R4. Such differences in directions of direct sound arrival are confirmed from BRIRs where direct components of \(B_{\text{left}}\) and \(B_{\text{right}}\) at R3 are of the same magnitude, whereas \(B_{\text{left}}\) at R4 presents larger amplitude than \(B_{\text{right}}\). The result also reinforces the plausibility of the present auditorium acoustics simulation.