Using Ray-tracing To Create Acoustical Energy Maps Ethan Adeniran, Sophomore | Faculty Mentor: Dr. Fernando Espinoza, Department of Physics and Astronomy
Hofstra University
The Art of Acoustic Imaging and Mapping
Results/Discussion
In a variety of scientific fields, the process of imaging is used to quantify and qualify data by providing a way to turn them into a graphical representation. In acoustics, engineers and designers often use beamforming techniques as a method to localize and quantify sound sources. This works by spatial filtering, which enhances signals in places where they are needed while also suppressing unwanted noise and interference. This method can also be adapted to predict acoustic parameters in rooms. By measuring the parameters in the fashion of an array, these parameters can be “mapped” on a model of the venue, which is known as acoustic imaging.
From the data obtained, several observations can be made. Firstly, looking at the RT60 data comparison, the simulation tended to produce data that fell below the expected value, but remain in line with the optimal values of a venue of this size. In fact, the simulated data fall more in line with the real values than the expected data as the expected data were skewed by averaging three trials, one of which tended to produce outlier results (which is reflected in RT values such as 2.03 seconds). Classical C80 Energy Map
The process of acoustic imaging begins with using an omnidirectional microphone array. After sending a signal, the data are then sent through a program that analyses the waveforms picked up by each individual microphone, thus giving data for the acoustic parameters. After receiving the data for the interactions, those data can then be mapped onto a three-dimensional model, or a two-dimensional image depending on the need.
In terms of clarity, a comparison is interesting as the data obtained by the simulation were extremely accurate in comparison to the expected data to the optimal values. This indicates that the expected data may have been wrong in some measurements, or that they were interpreted incorrectly. Regardless, the simulation proved to be a useful tool for clarity measurements.
Simulated D50 Map
Where the simulation didn’t reach expected values was in the measurement of the definition index. In areas such as the L1 and R1 locations, the data seemed to reflect each other. However, in all other areas, the percentages deviated greatly. We can infer that L1 and R1 have such high percentages due to their location relative to the sound sources. Because the receivers are located so close to the direct transmission of the source compared to the other receivers (including M1), this gave the L1 and R1 more consistent percentages.This may be best explained by the method in which I-SIMPA operates; namely needing very specific input values for absorption coefficients. Unfortunately, many of the documents for material absorption coefficients only consider frequency bands for 125 Hz, 250 Hz, 500 Hz, 1000 Hz, 2000 Hz, and 4000 Hz. Considering that the spectrum extends to 20,000 Hz, this lack of data probably limits the usefulness of the simulation.
Imaging provides many benefits as opposed to the classical methodology of measurement and analysis. Namely, imaging allows for more specified measurements due to the use of arrays instead of a singular microphone pointed in one direction or using an SPL meter. In this study, we will go one step further. We eliminate the use of microphones with ray-tracing techniques to simulate the propagation of sound waves to predict (or in this case, confirm) acoustic parameters previously measured classically. Classical RT60 Map As can be seen from the classical method of measurement, it’s difficult to pinpoint exactly where the boundaries for each acoustic parameter lie.
Methodology
Example graph of D50 index (definition index)
Optimal Measurements For a church, the ideal reverberation time is in the range of 1.4 seconds to 2.4 seconds depending on the size of the building and what a typical service entails. In our case, a range of 1.3 seconds to 2.0 seconds would be best. In terms of clarity, for speech intelligibility, the value of the C50 added to the noise floor should not be less than 55 dB or exceed 75 dB. The Definition Index (D50) can also be used to determine speech intelligibility, in which values above 50% indicate good intelligibility. For clarity or fullness of music (C80), optimal values should lie in the range of -4dB or +1dB. The expected simulated results based on the classical experiment conducted prior are:
In this case study, the program I-SIMPA will be used to carry out the simulation. I-SIMPA works by taking a 3-dimensional model of a venue, or “scene,” and then simulating the propagation of waves based on a variety of factors that affect sound, such as the absorption coefficients of materials in the venue, temperature, barometric pressure, and others.
Simulated C80 Map
Data for each of the punctual receivers (the areas where classical measurements were taken) were also obtained for more detailed comparison:
A model of the church was created using Sketchup 2022 and imported into I-SIMPA as a 3ds file.
Classical
Simulated
L M R 1.735 1.601 1.397 1.707 1.644 1.591 2.003 1.604 1.414
L 1.41 1.54 1.53
References
In I-SIMPA, the next step is to define the materials’ acoustic absorption coefficients, define sound sources, and receivers. After this is done, the simulation can be run. I-SIMPA simulates sound through hundreds of thousands of particles, as the way sound energy propagates through a medium. Finally, the simulation data can be turned into visual data that are then mapped onto the 3D model of the church.
1 2 3
The simulated results for the venue are as follows:
L 1 2 3
1 2 3
Simulated RT60 Map
1 2 3
M 1.35 1.45 1.43
R 1.36 1.40 1.45
Adeniran, Ethan X., Espinoza, Fernando. “Analysis of Worship Center Acoustic Quality for Audiences.” Hofstra Horizons for Undergraduate and Graduate Research, summer 2022. Picaut, Judicael, Fortin Nicolas. I-SIMPA (version 1.3.4) [Computer Software] Trimble, SketchUp Pro 2022 [Computer Software]
Data Analysis
Reverberation Time (RT60): Range of 1.41s – 2.00s Clarity (C80): Range of 5.69dB to 8.24 dB Definition (D50) - 64% - 74%
Classical D50 Energy Map
Other sources of “error” may include a lack of preciseness in measurements, due to limitations in access to building plans and materials. Another may be the lack of detail that can go into the actual model being used, as I-SIMPA often runs into computing issues the more surfaces (that are divided into triangles) that are introduced.
M
R
71.3% 61.4% 72.0% 64.2% 67.9% 65.5% 72.8% 74.3% 68.2%
L 7.24 5.98 6.35
M 6.05 5.69 8.24
R 6.90 6.46 6.47
L 1 2 3
1 2 3
M
R
74.1% 50.5% 64.7% 37.4% 42.8% 32.3% 41.3% 43.2% 46.4%
L 5.6 0.3 0.8
M 0.8 2.4 1.9
R -1.7 4.4 -3.7