Computer Modeling of Barrel-Vaulted Sanctuary Exhibiting Flutter Echo with Comparison to Measurements
2.1.1. Room Configuration
2.1.2. Measurement Equipment
2.1.3. Source and Receiver Locations
2.2. Computer Modeling
2.2.1. Geometrical Acoustics (GA) Methods
2.2.2. GA Computer Modeling Methodology
2.2.3. Wave-Based Methods
2.2.4. Wave-Based Computer Modeling Methodology
2.3. Signal Processing of Room Impulse Response
- Spectrogram Analysis: Spectrograms were generated from 48 kHz sampled RIR data using a 10 ms Hann window with 120 sample overlap.
- Reverberation Time: Reverberation times (T(20) and T(30)) were calculated from the 48 kHz sampled RIR data for the 125–8000 Hz octave bands using the ITA toolbox .
- Energy Decay Curve: The energy decay curves were generated from the 48 kHz sampled RIR data using the ITA toolbox. The curves were normalized and plotted in dB using P = 20 over a 40 dB reduction in SPL.
2.4. Wavelet Multi-Resolution Analysis
- The differences between the wavelet types which they applied were insignificant, therefore, any of the tested wavelet families could be applied with similar results.
- The length of the wavelet had a significant effect on the uniformity of the results, where wavelets with longer support gave rise to more consistent results.
3. Results and Discussion
- R01 and R04: As both of these figures are the same distance from the sound source, with one located on the aisle and the other located off the aisle, comparison between these two points demonstrates the non-diffuse nature of the room.
- Original and Panel (with R01 and R04): In order to demonstrate the changes in the room acoustics as a result of the addition of acoustical panels, some figures feature side-by-side comparisons of the original room configuration and the room configured with panels as shown in Figure 4.
- R03, R04 and R05: These three receiver locations represent three different heights at the same location in the room as shown in Figure 3. This comparison demonstrates the unique behavior of the flutter echo at different heights relative to the source height.
3.1. RIR Spectrogram
- Behavior of the room on and off the aisle: Comparison of Figure 7 and Figure 8, demonstrates the non-diffuse nature of the room. As stated earlier, both receiver points R01 and R04 are the same distance from the sound source, however, because of their location with respect to the barrel-vaulted ceiling, their spectrograms display very different behaviors.In high frequencies, above 4000 Hz, the measured original R01 and R04 spectrograms exhibit similar behavior, with the majority of the energy having died out by 0.5 s. Below 4000 Hz, the behavior of the two locations are quite different. In the audience, the signal dies out almost completely by 1.5 s, while in the aisle, it remains well beyond 4 s. Additionally, the signal is characterized by a periodic pattern representative of the flutter echo present in the aisle. Furthermore, along the aisle, it is possible to identify the comb filter behavior expected from a flutter echo.
- Behavior of room before and after the addition of panels: In order to demonstrate the changes in the room acoustics as a result of the addition of acoustical panels, some figures feature side-by-side comparisons of the original room configuration and the room configured with panels as shown in Figure 1.Similar to what was observed in the comparison of R01 and R04, at higher frequencies (above 4000 Hz), the addition of the panels had very little effect on the spectrogram. Below 4000 Hz, in the audience area, the addition of the panels reduces the energy, such that the signal is essentially eliminated after 1.5 s. On the aisle, the effect of the panels is more pronounced, with the primary effect being to eliminate the majority of the late decay energy in the 250–2000 Hz octave bands after 2 s. The panels also have a secondary effect of reducing the amplitude of the peaks from 0.5 to 1.5 s.These results indicate that the panels had the desired effect of reducing the RT along the aisle without completely eliminating the spacious feel of the room promoted by the flutter echo.
- Comparison of the GA and wave-based modeling with the measured data: The spectrograms provide a means of comparison of the similarities and distinctions between the measured data and the two different modeling techniques, GA and wave-based. Comparison between measured and modeled response before 0.5 s highlights specific early behaviors (before 0.5 s) and later behaviors. Before 0.5 s, both models contain more energy above 8 kHz than the measured data, with Odeon predicting much more sustained high frequency energy. It is important to note that above 8 kHz, both Odeon and the wave-based model use ray-tracing techniques. Also, the measured data has a band of higher energy sustained past 0.5 s around 6500 Hz, which is not identified in the wave-based model.Most significantly, the very distinct pattern of the flutter echo detected in measurements on the aisle in Figure 8, are clearly identified in the wave-based model, but are not present in the spectrogram of the Odeon model RIR.
3.2. RIR Reverberation Times
3.3. Energy Decay Curves
3.4. Wavelet Multi-Resolution Analysis
3.4.1. Comparison of Flutter Echo On and Off the Aisle
3.4.2. Comparison of Flutter Echo Before and After the Addition of Panels
3.4.3. Structure of Triplets Based on Receiver Height
Conflicts of Interest
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|Material||31 Hz||63 Hz||125 Hz||250 Hz||500 Hz||1 kHz||2 kHz||4 kHz||8 kHz||16 kHz|
|Wavelet Level||Octave Band (Hz)|
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Lai, H.; Hamilton, B. Computer Modeling of Barrel-Vaulted Sanctuary Exhibiting Flutter Echo with Comparison to Measurements. Acoustics 2020, 2, 87-109. https://doi.org/10.3390/acoustics2010007
Lai H, Hamilton B. Computer Modeling of Barrel-Vaulted Sanctuary Exhibiting Flutter Echo with Comparison to Measurements. Acoustics. 2020; 2(1):87-109. https://doi.org/10.3390/acoustics2010007Chicago/Turabian Style
Lai, Heather, and Brian Hamilton. 2020. "Computer Modeling of Barrel-Vaulted Sanctuary Exhibiting Flutter Echo with Comparison to Measurements" Acoustics 2, no. 1: 87-109. https://doi.org/10.3390/acoustics2010007