Suitable data for spatial wave field analyses in concert halls need to satisfy the sampling theorem and hence requires densely spaced measurement positions over extended regions. The described measurement apparatus is capable of automatically sampling the sound field in auditoria over a surface of 5.30 m × 8.00 m to any appointed resolutions. In addition to discussing design features, a case study based on measured impulse responses is presented. The experimental data allow wave field animations demonstrating how sound propagating at grazing incidence over theater seating is scattered from rows of chairs (seat-dip effect). The visualized data of reflections and scattering from an auditorium's boundaries give insights and opportunities for advanced analyses.
1. Array-measurements in architectural acoustics
Measurements in general are a core feature to back up theories and to support conclusions. In both cases, practical and standardized room acoustical measurement surveys are frequently limited to examining a relatively small number of selected positions. The reasons for this practice are very understandable as obstructions created by rows of seating and complex geometries such as balconies make it costly and time consuming to refine the measurement coverage. In specialized research (e.g., to discuss measurement uncertainties or to visualize complex sound fields for wave field imaging,) it may be necessary to cover larger areas in detail to satisfy the Nyquist-Shannon sampling theorem in space. Depending on the type and focus of investigation, different approaches have been previously pursued to sample the sound field in concert halls.
With the initial goal of collecting a data set that can be used to decompose the sound field into plane waves, de Vries et al.1 measured room impulse responses (RIRs) along a line array. From the measured data, it was observed for the first time that room acoustic single-number parameters fluctuated significantly over relatively small spatial distances.
In order to survey the range of acoustic conditions within the dimensions of a concert hall, Akama et al.2 collected data in different auditoria and measured up to almost 1900 RIRs. To measure the transfer function from a respective source position to each seat in the investigated auditoria, they manually moved the microphone in steps throughout the entire audience areas. The data were used to determine the statistical properties of the derived single-number parameters and determine the minimum sample size required to discern the spatial differences in the sound field.
The challenges of covering large dimensions in architectural acoustics while also collecting high-resolution data can be met with measurements in model scale. The apparatus used by Xiang et al.3 to investigate the acoustic coupling of two room volumes in a 1:8 model scale shows how the sound field can be sampled with high accuracy using a motorized microphone that is automatically moved in two dimensions.
With the goal of collecting natural stimuli for listening experiments and investigating how the acoustic conditions depend on the position in different rooms, Witew et al.4 conducted acoustic measurements in different concert halls for about 100 source-receiver combinations. The general measurement strategy is comparable to the method used by Akama et al.2 Although this strategy allows the collection of a large number of RIRs in different auditoria, it requires extensive manual effort. Furthermore, without sophisticated tracking strategies, the uncertainty of the microphone position is limited, at best, to the dimensions of the reference object (i.e., to the size of a seat). Even if a floor plan were available, the complex geometry of auditoria would make it difficult or impossible to determine the exact microphone position (say in Cartesian coordinates). This intrinsic uncertainty may not be sufficient for some questions. To derive a better estimate of the surveyed receiver positions, a trilateration strategy based on measured distances of the microphone to known marker positions can be used. Although distances can be measured readily using common laser-interferometry devices, determining accurate positions of the reference markers is time consuming. Even though the authors have used this strategy yielding plausible microphone positions, determining the estimates' accuracy is not readily accessible without ample expertise in engineering geodesy.
When detailed knowledge of the measurement position is of concern, the use of measurement devices to automatically place and move microphones can be an option. Witew and Vorländer5 placed 24 microphones on an automated xy-table which allowed the sampling of the sound field over a surface of 2.1 m × 2.4 m. Although data collected with this two-dimensional setup provide novel information, the comparison of array dimensions to the general size of auditoria may nurse the wish for larger sampling regions. Larger measurement devices, however, make it increasingly challenging to determine an absolutely accurate microphone position due to relative manufacturing tolerances. It is worth noting that sound scattering and reflections from the supporting structures of larger devices become an increasing factor as well.
This paper presents a measurement system that automatically and precisely samples a sound field over an extended area in high resolution. The design attempts to address the inherent concerns of larger measurement devices. The robotic microphone array allows the collection of data that offers a new perspective on versatile aspects of sound propagation in rooms. It is for the first time in room-acoustics (to the authors best knowledge) that the scattering effect from theater seating on sound waves passing at grazing incidence is demonstrated from experimental data at this scale and resolution. The discussion of reflections and scattering from an auditorium's boundaries show how many wave effects can be demonstrated based on the measured and scanned data. A quantitative analysis is generally possible but should be a future subject to an independent discussion. Both wave-based and geometrical acoustic simulation tools can benefit from this experimental capability as the collected data can provide the foundation for further development and important validation. The shown wave field animations may provide a platform for researchers, practitioners, or students to develop new insights and opportunities for advanced analyses.
2. Functionality of the measurement device
In an attempt to create a functional measurement tool for specialized investigations of larger sampling areas, the measurement robot shown in Fig. 1 (top left) was designed. Made from aluminum trusses, commonly used in stage equipment, the device is capable of automatically sampling the sound field in rooms over a surface of 5.30 m × 8.00 m. The truss profiles have a triangular cross section with a width of 220 mm and a height of 195 mm. The three supporting tubes along the length of each truss have a diameter of 35 mm. As the setup in Fig. 1 (top right) shows, the apparatus consists of a frame structure and a central cross beam which are supported by four 2 m-tall pedestals.
(Color online) Measurement device to sample the sound field in rooms with detailed views showing the driving mechanism and the mounting of the measurement robot. Top left: Measurement setup in the large hall of Eurogress Aachen. Top right: Schematic drawing of the setup (not to scale). Bottom left: Rack and pinion actuator to move the robot. Bottom center: Roller bearing and sliding support of the carbon truss carrying the microphones. Bottom right: Mounting of the KE-4-type microphones in carbon tubes and attachment to the carbon truss.
(Color online) Measurement device to sample the sound field in rooms with detailed views showing the driving mechanism and the mounting of the measurement robot. Top left: Measurement setup in the large hall of Eurogress Aachen. Top right: Schematic drawing of the setup (not to scale). Bottom left: Rack and pinion actuator to move the robot. Bottom center: Roller bearing and sliding support of the carbon truss carrying the microphones. Bottom right: Mounting of the KE-4-type microphones in carbon tubes and attachment to the carbon truss.
A core feature of the apparatus is a sliding carriage that is hanging from a rail on a central cross beam. The carriage moves along the x axis (see Fig. 1, top) by means of a motorized pinion that acts on a fixed rack running parallel to the central cross beam (Fig. 1, bottom left). Orthogonal to the central cross beam, along the y axis, there is an 8 m carbon truss which is supported at the center and both ends. Centrally mounted to the carriage (see Fig. 1, bottom left), the carbon truss can be moved along the y axis over a distance of 30 cm by a spindle drive with a shaft joint. The carbon truss is held in place at both ends with free movement provided by a sliding support in the y-direction and a rolling support through a rail in the x-direction (see Fig. 1, bottom center).
There are 32 vertical drillings in 25 cm steps along the length of the carbon truss's lower edge. With the use of adjustable collars, a 1 m-long carbon tube hangs from each of the 32 slots with a microphone mounted on the lower end (see Fig. 1, bottom right). This setup allows free movement of an individual microphone over a surface of 5.3 m × 0.3 m. The fixed microphone spacing of 25 cm makes a small overlap between the sampling areas of two neighboring microphones possible. From a practical perspective this overlap may be neglected, however, it ensures that the 32 microphones may sample a composed surface of 5.30 m × 8.00 m without gap to any appointed resolution.
As previously noted, manufacturing tolerances and the need for a relatively large measurement apparatus prompted efforts toward a method for determining the exact sampling position. In order to create the data base for an acoustic trilateration, six small loudspeakers are mounted into the four stands and into the elevated frame of the apparatus. The distance between a microphone and each one of the six “localization”-loudspeakers can be calculated from the sound's propagation time, which can be read from the measured impulse responses. The distance data provide the foundation for determining the most accurate estimate of the actual microphone position through non-linear least squares optimization. First trials suggest that the microphone position can be determined in post-processing with an accuracy to a few millimeters.
The measurement apparatus can be assembled and disassembled in about 2 h each with a trained team of four people. To sample the sound field over a surface of 5.30 m × 8.00 m in a rectangular 5 cm-grid, exactly 530 individual measurement runs using 32 microphones are necessary. The robot travels from one position to the next between each subsequent measurement. With 32 microphones mounted in 25 cm increments along the carbon truss, the robot makes 5 consecutive measurement runs in 5 cm steps to sample a length of 8.00 m along the y axis. Sampling the entire surface at this resolution requires about 4 h. In this period of time, 118 720 impulse responses are measured. The measurements feature the primarily interesting set of 16 960 FFT-degree-17 RIRs, (fast Fourier transform (FFT), 217 samples ≈ 2.9 s length) and the 101 760 FFT-degree-16 impulse responses (≈1.4 s length) that are used to measure the sound propagation time as an input for the acoustic multilateration. As a result, a grand total of about 8 h, including provisions for mounting and demounting, is needed to conduct a full set of sound field measurements.
3. Sound field visualization
The additional benefit from measurement data collected with microphone arrays is not only due to the larger amount of available data to analyze, but also due to the geometric relation the additional measurement positions have to each other. The RIRs collected with the device described here mark no exception in this regard. The graphical presentation of four-dimensional-data (two spatial dimensions and the amplitude of the impulse response over the running time), however, poses known challenges with presentation modalities in most cases providing only three dimensions for simultaneous display. The microphone data (i.e., RIR at a given time) over the spatial dimensions of the measurement array's sampling area can be shown effectively so that each presented pixel refers to a corresponding sampling position. The energy of the impulse response can be coded in color for a given time, leading to graphical representations such as the ones shown below (e.g., Figs. 2 and 3). Animations (see Mm. 1) can be inspected to further show the RIR of each location over time.
(Color online) Bandpass filtered wave fronts [62.5–2000 Hz] as they propagate through the measurement array at 11 ms. Running time starts with the entry of the direct sound into the sampling area. Animation is shown in Mm. 1.
(Color online) Bandpass filtered wave fronts [62.5–2000 Hz] as they propagate through the measurement array at 11 ms. Running time starts with the entry of the direct sound into the sampling area. Animation is shown in Mm. 1.
(Color online) Bandpass filtered wave fronts [62.5–2000 Hz] as they propagate through the measurement array at 39 ms. Running time starts with the entry of the direct sound into the sampling area. Animation is shown in Mm. 1.
(Color online) Bandpass filtered wave fronts [62.5–2000 Hz] as they propagate through the measurement array at 39 ms. Running time starts with the entry of the direct sound into the sampling area. Animation is shown in Mm. 1.
Animated measurement data showing how sound propagates in an auditorium. The comparison of two repeated measurements shows how the presence of chairs changes the sound field. An energy histogram shows how the energy distribution differs between measurements. The animation is a file of type “mp4” (57.4 Mb). A version in high resolution is archived.6
Animated measurement data showing how sound propagates in an auditorium. The comparison of two repeated measurements shows how the presence of chairs changes the sound field. An energy histogram shows how the energy distribution differs between measurements. The animation is a file of type “mp4” (57.4 Mb). A version in high resolution is archived.6
Based on Euler's wave equation of linear acoustics, any RIR is already a common manifest of sound propagation in rooms as the distance sound travels—being reflected and scattered from the room's boundaries—can be acquired from the RIR's running time. Although the available array data shown in Figs. 2 and 3 only provides a snap shot of the RIRs at a given moment in time, it is the same relationship between sound pressure, time, and space that shows how sound propagates through the room and, respectively, through the array. The curvature of the wave fronts in the still images clearly indicates spherical wave propagation. The energy is color coded and shown in decibels relative to the highest absolute energy recorded in all of the measurements. Although the measurement peak to noise ratio is about 60 dB, for purposes of presentation the shown range is limited to 35 dB.
The images in Fig. 2 show the first wave front (i.e., the direct sound) sent into the room from an equalized sound source. The equalization ensures the presentation of a signal-theoretic perfect impulse within the bounds of the displayed frequency range (62.5–2000 Hz-octave bands) as it propagates through the array. The sequence of four consecutive concentric wave fronts suggests that the direct sound is immediately followed by reflections that are diverted only by a small amount in distance and direction. The auditorium's stage or ground floor come into consideration as responsible surfaces. In contrast, Fig. 4 (left) shows the impulse responses at a later moment in time (t ≈ 34 ms after the direct sound entered the sampling area) where at least three overlapping wave fronts can be seen. Based on their lack in concentricity, it can be argued that the delayed wave fronts are a result of sound reflected from different boundaries farther apart from each other. The delay and the direction of these wave fronts suggest that the obtuse angled surfaces of the stage enclosure and the ceiling are responsible for these reflections. The propagation paths are shown in dotted lines in Fig. 4 (right).
(Color online) Sound field 34 ms after the direct sound entered the sampling area. The propagation paths of the overlapping wave fronts are shown in dotted lines in the floor plan.
(Color online) Sound field 34 ms after the direct sound entered the sampling area. The propagation paths of the overlapping wave fronts are shown in dotted lines in the floor plan.
3.1 Grazing sound over theater seating
Since the first quantitative survey,7 a multitude of investigations have discussed the effect of sound passing at grazing incidence over seating. A broad consensus exists that its prominent feature is low frequency attenuation.8 A graphic account of the grazing sound propagation over time can be inspected most effectively in Mm. 1. Measured array data that were collected in an approx. 14 500 m3 auditorium with floor plan presented in Fig. 4 (right) is shown. The animation visualizes energy distributions of two measured sound fields, i.e., the first 100 ms of measured impulse responses beginning at t ≈ 0 ms with the direct sound about to propagate through the array. The hall was completely empty of chairs on the main floor at the time of the first measurement. The data concerning the hall with no chairs are shown in the left animation tile. The second measurement, shown in the right tile, was conducted immediately after the first measurement and features the room in virtually the same condition, except that in the transition period between measurements stackable chairs as shown in Fig. 1 (top left) were placed within the perimeter of the array. The difference in sound levels caused by different room configurations is most evident in the time and space immediately following the direct sound wave when comparing both animated impulse responses. The left animation (without chairs) shows significantly less energy (in blue) in the 20 ms after the passing of the direct sound compared to the same period in the right animation (with chairs). Figure 2 illustrates still images of the spatial sound field where the difference in energy level after the direct sound is clearly visible as well. The right animation also shows the successive release of five secondary waves following the direct sound that propagate back to the front of the sampling area. The secondary waves' origins match the locations at which the rear five rows of seating are placed at. The wave released from the first row of seating cannot be seen as its propagation path (back to the stage of the auditorium) lies outside the sampling area. The energy distribution is presented in the third tile in the lower region of the animation. Still images are shown in Fig. 5. It may be understood as a histogram featuring the 16 960 color coded energy pixels shown in each of the two sound field tiles, except that the dynamic range is expanded from 35 to 50 dB. The influence of seating is evident in the differences in levels between the two measurements (Fig. 5, left).
(Color online) Energy distribution of the measured sound fields. (Left) 11 ms after the direct sound entered the sampling area. (Right) 39 ms after the direct sound entered the sampling area.
(Color online) Energy distribution of the measured sound fields. (Left) 11 ms after the direct sound entered the sampling area. (Right) 39 ms after the direct sound entered the sampling area.
3.2 Influence of the apparatus on the measured quantity
Upon close observation, concentric waves emanate from the four corners of the sampling area after the direct sound passes [see Mm. 1 and Fig. 2 (left)]. The emanating waves mark backscattered high frequency sound ( 1000 Hz octave band) from the pedestals of the measurement apparatus. It may be rated as negative, that the measuring system impairs the measured quantity. While this remains an unwanted effect, it seems generally unavoidable in all acoustic measurements. The effect becomes evident toward high frequencies. In the frequency range featured in Fig. 2, the disturbance has a level of approximately −25 to −20 dB relative to the highest energy that was measured.
3.3 Sound propagation in concert halls
A third and fourth reflection become visible (around 30 and 37 ms) after the direct sound and first reflections that were discussed earlier. Both of the later reflections arrive from the same frontal direction as the direct sound, only that they seem to be traveling faster than the other waves. The contrast in apparent propagation velocity is an indication that both of the later reflections are traveling oblique to the measurement plane. The algebraic sign of the oblique angle of incidence is ambiguous due to the two-dimensional arrangement of the microphones. First, the wave front arriving at t ≈ 30 ms (in Fig. 3 at y ≈ 3.5 m) can be clearly identified in both measurement scenarios. The wave front arriving at t ≈ 37 ms (in Fig. 3 at y < 1.0 m) is only prominent in the measurement without chairs. In the measurement with chairs it is only faintly visible as it enters the sampling area but quickly dissipates as time progresses. Based on the same direction of propagation and the delay of 7 ms, which corresponds to a detour of approximately 2.4 m, this set of wave fronts mark the sound that is first order reflected from the ceiling. The fourth wave front appears to also be a second order reflection from the ground floor which well corresponds to the delay, given that the microphones were placed at an ear height of approximately 1.1 m above the ground. When the floor is obstructed with chairs underneath the array in the second (right) measurement, the fourth wave is quickly scattered and reduced in amplitude so that it is only evident for microphones at the front of the sampling area. The setup without chairs (left tile) allows a strong specular reflection from the ground floor which leaves the fourth wave front intact as it propagates through the array from beneath.
In a second aspect, the supposed first order ceiling reflection (30 ms) partially dissipates as it propagates through the array. Figure 1 (bottom center) offers a glimpse at the coffered ceiling in parts fitted with diffusing elements. As the individual coffer elements are limited in size, they are effective for a likewise limited range of emergent angles. Different regions of the sampling area are therefore differently irradiated by sound reflected from the ceiling elements.
At t ≈ 44 and 45 ms, two waves from the side and the rear enter the array. The two delayed waves mark reflections from the balcony façades, indicated by the direction of propagation, delay of the waves relative to the direct sound, and the knowledge that the array was erected around 5 m in front of the balcony (see Fig. 1, top left).
As the running time of the impulse response progresses, the reflection density increases significantly and only very strong and insulated reflections can be clearly assigned to a sequence of room surface reflections (e.g., a reflection of the left reversed splay entering at t ≈ 67 ms or a reflection from the rear wall entering at t ≈ 81 ms). The energy histogram of the animation shows that the influence of the chairs is less pronounced as the measurement time increases (see Fig. 5, right). The energy distributions for both measurements are fairly similar in shape, the only difference being a small ≈1 dB-decrease in the curve representing data from the measurement with chairs to lower energy levels. The decrease in energy level may be due to the additional absorption that was introduced to the room by placing chairs on the main parquet.
At t = 50 ms and at t = 80 ms, respectively, a gray propagation wave is drawn into the left and right animation tiles. The gray waves mark the 50 and 80 ms time limit after the direct sound passed which is relevant for a number of parameters such as speech or music clarity (C50 or C80). Reflections that propagate through the array “above” the plotted gray curves (i.e., 50 or 80 ms after the direct sound) would formally be recognized as detrimental by the respective clarity parameters.
4. Concluding remarks
In this publication we present a measurement apparatus capable of automatically sampling the sound field in rooms over an extended region. In a case study the collected data are processed to prepare animations and images that visualize the sound field in an auditorium. The sampled array data allow the identification of a number of wave fronts and their respective propagation paths in the room. The effectiveness of sound reflecting and sound scattering surfaces is discussed. In comparing how the direct sound of an impulse response propagates through the auditorium with and without chairs on the main floor, a new high resolution perspective on grazing sound propagation over theater seating (i.e., seat-dip effect) is given in spatial and temporal domains based on actually measured data.
Acknowledgments
Parts of this study have been presented at the meeting of the German Acoustical Society (DAGA) in March 2016. The authors wish to thank the staff of the mechanical and electrical workshop of ITA for constructing the apparatus and active support of this project. Measurements have been conducted with the help of students and employees of ITA. The works of Jakob Hartl (J.H.) and F.T. stand out in this respect. J.H. conducted measurements, tested the device for error resilience, and proof read the manuscript. F.T. designed the software control for the measurement apparatus. Thanks to the administration of Eurogress Aachen, who supported this work in enabling us to conduct measurements in their auditorium. Each author contributed in a different way to the whole of this work. I.B.W. is responsible for the measurement devices design, the data analysis, and in significant parts for the measurements. The interpretation and discussion of the results was done jointly by all of the authors.