Scattering in Room Acoustics and the Related Activities in ISO and AES

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2 Scattering in Room Acoustics and the Related Activities in ISO and AES Jens Holger Rindel Ørsted DTU, Acoustic Technology, Technical University of Denmark, Building 35, Ørsted Plads, DK-800 Kgs. Lyngby, Denmark Scattering from the surfaces in a room is known to be of great importance for the acoustic quality of the room. In order to deal with this in a scientific way there is a need for definitions of concepts to characterise the scattering and for related measuring methods. Through the co-ordinated efforts of two working groups under ISO and AES a basis for scattering has been established. ISO has derived a method for measuring the random-incidence scattering coefficient in a reverberation chamber. This measure can be used to characterise the degree of scattering due to the roughness of a surface. AES has derived a method for measuring the diffusion coefficient of a surface as a function of the angle of incidence. This measure can be used to characterise the uniformity of the scattering from a surface. The practical aspects of the measuring methods and some of the inherent problems are discussed. INTRODUCTION Together with the sound absorption characteristics, the acoustic scattering from surfaces is very important in all aspects of room acoustics, e.g. in concert halls, sound studios, industrial halls and reverberation chambers. Already W. C. Sabine knew this by intuition more than one hundred years ago when he was involved in the design for Boston Symphony Hall. Scattering of sound can be achieved by single elements like columns, statues etc. or by surfaces with a sufficiently rough structure like QRD diffusers or by diffraction effects along the edges of panels. Until now the work has focused on the surface scattering, whereas single diffusers have not been dealt with. Two different measures are introduced with somewhat different applications: One measure gives the quantity of scattered reflections, which may be sufficient for use in room acoustic computer models. The other measure is intended mainly for evaluation of the quality of sound diffusers and in situations where it is important to achieve scattered first-order reflections, e.g. in sound studios. The main features of the two new measures are described in the following. THE SCATTERING COEFFICIENT A working group under ISO has prepared a draft standard, which was accepted with some comments by the ISO member bodies in the fall 000 [1]. The method describes how to measure the randomincidence scattering coefficient in a reverberant room and it is based on []. The scattering coefficient is defined as one minus the ratio between the specularly reflected acoustic energy and the total reflected acoustic energy. When measured in an approximate diffuse sound field it is called the random-incidence scattering coefficient with the symbol s and values between 0 and 1. The scattering coefficient describes the degree of scattering due to the roughness or irregularity of a surface the scattering due to diffraction from the edges is not included. The Measurement Method The measurements are performed in a reverberation chamber like a double set of absorption measurements. The test sample must be circular and it is placed on a highly reflecting base plate with the same diameter. The reverberation time is measured with and without the test sample on the base plate, and the randomincidence absorption coefficient α s is determined. The base plate with the test sample is mounted on a turntable, and a new pair of measurements is made with continuously rotating test sample/base plate. Alternatively the turntable is turned in 7 steps of 5 for each new measurement. With different positions of the test sample the scattered energy is not correlated. The impulse responses are measured and by synchronised averaging only the correlated (specular) part of the impulse responses is obtained and the reverberation time is derived. Thus, the so-called specular absorption coefficient α spec is determined. In this measurement the scattered energy is treated as an additional energy loss that is included in the specular absorption coefficient. Thus α spec α s. Finally, the random-incidence scattering coefficient s is calculated from: s = 1 (1 α spec ) (1 α s ) (1)

3 Some Limitations The preferred area of the test sample depends on the volume of the room, but the minimum is 10 m for a full size measurement. However, for practical reasons it is often advantageous to use a physical scale model. The absorption of the test sample should be low in order to obtain acceptable measurement accuracy. The air attenuation may cause a reduced accuracy at high frequencies in the case of scale measurements. The structural dept of the test sample should not exceed d / 16, where d is the diameter of the sample. Still, the variation of height along the perimeter of the sample can cause additional edge scattering that may lead to a measured scattering coefficient higher than unity. In general the scattering coefficient is frequency dependent with low values at low frequencies and higher values at high frequencies. THE DIFFUSION COEFFICIENT A working group under AES has prepared an information document [3] that describes how to measure the surface scattering uniformity in a free field environment. The considerations that have lead to the proposed diffusion coefficient are described in [4]. The diffusion coefficient is derived from the autocorrelation function of the polar response measured on a semicircle or a hemisphere and it has the symbol d. It can take values between 0 and 1, and d = 1 means that the polar response is completely uniform. The Measurement Method The measurements are performed in an anechoic room with the receivers on an arc with a preferred radius of 5 m and an angular resolution of max. 5. The source positions should be in a distance of 10 m. One problem is that the polar response depends on the size of the test specimen and the distance to the source and receivers. Thus, it is important to follow the described procedure as closely as possible. The directional diffusion coefficient d θ is derived for one particular source position and θ is the angle of incidence. If p i denotes the sound pressure measured at receiver i and there is a total of n receivers, then d θ is i 4 pi 4 ( pi ) pi i dθ = () ( n 1) i The random-incidence diffusion coefficient d is the mean result for a number of different source positions with an angular separation of max. 10. Some Limitations The measurement method does not distinguish between surface scattering and edge scattering - both are included. Thus it is important that the test sample is large enough so that surface effects rather than edge effects are prominent in the scattering. COMPARISONS BETWEEN THE TWO MEASURES There is no direct relationship between the scattering coefficient s and the diffusion coefficient d. A high value of d implies that s is also high, whereas a high value of s can be combined with any value of d. For example a saw tooth profile can redirect the reflection, so s is high, but the scattering is far from uniform, so d is low. Both measures can be calculated from the reflection directivity. However, for calculation of the scattering coefficient it is also necessary to know the reflection directivity from a flat reference surface with the same area as the test sample, see [5]. CONCLUSION Through the co-ordinated efforts of two working groups under ISO and AES a basis for scattering has been established. It has been agreed that there is a need for two different measures in order to characterise the acoustic scattering from surfaces. The measurement methods may be used for test samples either in full scale or in an appropriate scale ratio. It is believed that the new measures of surface scattering will improve the basis for good design in room acoustics. REFERENCES 1. ISO/CD 17497:000. Acoustics Measurement of the randomincidence scattering coefficient of surfaces.. M. Vorländer & E. Mommertz. Definition and measurement of random-incidence scattering coefficients. Applied Acoustics 60 (000) AES-4id-001. AES information document for room acoustics and sound reinforcement systems Characterization and measurement of surface scattering uniformity. J. Audio Eng. Soc. 49 (001) T.J. Hargreaves, T.J. Cox, Y.W. Lam & P. D Antonio. Surface diffusion coefficients for room acoustics: Free-field measures. J. Acoust. Soc. Am. 108 (000) E. Mommertz. Determination of scattering properties from the reflection directivity of architectural surfaces. Applied Acoustics 60 (000)

4 Contrasting Surface Diffusion and Scattering Coefficients Trevor J. Cox a,b, Peter D Antonio b a School of Acoustics and Electronic Engineering, University of Salford, Salford, UK. b RPG Diffusor Systems Inc., 651-C Commerce Drive, Upper Marlboro, MD 0774, USA. In recent years, several coefficients to measure the degree of scattering or diffusion from a surface have been developed. These have been developed to meet the needs of diffuser manufacturers, room designers and geometric room acoustics modellers. The coefficients give a frequency dependent measure analogous to the absorption coefficient. Two of these coefficients are, or are about to be, enshrined in international standards. Very little has been published, however, directly comparing the coefficients and so their relative merits are difficult to judge. Consequently, this paper will contrast the different coefficients, demonstrating their strengths and weaknesses. A simple prediction model for the free field Mommertz and Vorländer scattering coefficient for Schroeder-style diffusers will be given; this leads to a diffuser design methodology. In general, it appears that this scattering coefficient gives significantly larger values than a diffusion coefficient based on polar response uniformity. Prediction and measurement results on other surfaces, such as curved surfaces and rectangular battens, will enable guidance to be given as to the applicability of these coefficients. None of the coefficients appears to be perfect and it will be shown that the correct choice is application dependent. INTRODUCTION The first ever international standard on the characterisation of surface scattering/diffusion was published this year [1]. AES-4id-001 characterises diffusion as the uniformity of polar distributions. Characterisation is done in terms of the autocorrelation function []. In this respect, it is meant to be a quantifier of diffusion quality for diffuser designers and installers. Current ISO WG5 is working on standardising a random-incidence scattering coefficient method [3]. The scattering coefficient uses the variance of the sound field when the test surface is moved. It is intended to be used in geometric room acoustic models to improve the prediction accuracy. Also discussed in this paper is the approach of Mommertz [4], who suggested a method for obtaining scattering coefficients from polar responses. The above methods have tended to be developed in isolation. The intention of this paper is a comparison of these different coefficients to highlight their some of their advantages and disadvantages. SCHROEDER DIFFUSERS Schroeder diffusers can be approximately modelled as variable impedance surfaces using a simple Fourier approach. This then forms a convenient test bed for the different scattering and diffusion coefficients. Consider the ISO technique using surface movements. For this test bed, a free field formulation is used and surface translation rather than rotation is implemented. Therefore the philosophy of ref [3] is preserved, but not the exact method. Under these conditions, the scattering coefficient δ is: N 1 jkd δ e n (1) 1 N 1 Where N is the number of wells per period, k the wavenumber and d n the depth of the n th well. This is a sum of the reflection coefficients, no reference to well position is given because the receiver is fixed in the specular reflection. Furthermore, the scattering coefficient according to this formulation is independent of incident angle. The best scatterers have Diffusion/scattering ISO AES PRD AES plane Mommertz f (Hz) Figure 1. Schroeder diffuser test bed for modified Primitive Root Diffuser (PRD)

5 a vanishing sum of the reflection coefficients, which is achieved if the reflection coefficients are evenly spaced around the unit circle. This is achieved for modified versions of the primitive root diffuser (PRD) [5,6]. Figure 1 shows some typical results using a PRD. Comparing the ISO scattering and AES diffusion coefficients, it can be seen that a numerically smaller value is found for the AES coefficient. There is good agreement, however, as to the frequency at which the PRD starts dispersing sound (00Hz) and the flat plate frequency (3kHz). At many frequencies, the PRD is scattering considerable sound energy from the specular zone, but not evenly. This is why the AES coefficient is significantly less than the ISO coefficient, and why the AES coefficient is a better test of diffuser quality. SCATTERING COEFFICIENTS FROM POLAR DISTRIBUTIONS The ISO and AES coefficients satisfy two different needs. The former to give a number required for more accurate computer modelling, the later to allow proper evaluation of diffuser quality. It would be useful to be able to translate between the two coefficients, even knowing that there will be pathological cases that will cause problems. Mommertz forwarded a method [4], using the correlation between the pressures scattered from a test sample and a plane surface. This allows the scattering coefficient to be obtained from polar responses. In the Schroeder diffuser test bed, Fig. 1, the Mommertz coefficient matches the ISO coefficient well at high frequencies, but less so at low frequencies. This has also been tested for a variety of surfaces in measurement and with BEM predictions. In Figure the scattering coefficient for a N=7, 1D Scattering coefficient f (Hz) Mommertz ISO Figure Flutterfree scattering coefficients 4000 Mommertz s method of getting scattering coefficients from polar responses yields values similar to randomincidence measurements following the proper ISO procedure. Results on other surface types have also shown that this may be a route to enable the randomincidence scattering coefficient to be predicted using free-field predictions models such as BEMs. CONCLUSIONS The ISO and AES coefficients are contrasted below. They have different philosophies and therefore different uses. Efforts to enable translating between the coefficients are on-going. ISO scattering coefficient AES diffusion coefficient Uses For computer modelling Assessing diffuser quality Large surfaces, smallsmall surfaces, large irregularities irregularities Advantage Quick measurement Can be predicted Limitations Redirection seen as dispersion Ignores phase dispersion Problems Undefined meaning interpreting single of intermediate plane scatterers with values a hemispherical Achieving Far field coefficient measurement Values > 1 difficult ACKNOWLEDGEMENTS Thanks to Janina Fels and Marcio Gomes from Institut für Technische Akustik, RWTH Aachen for carrying out the measurements. REFERENCES 1. AES-4id-001. J.Audio.Eng.Soc. 49(3) (001).. T J Hargreaves, T J Cox, Y W Lam and P D'Antonio. J.Acoust.Soc.Am. 108 (4), (000). 3. M Vorländer and E Mommertz. Applied Acoustics. 60() (000). 4. E Mommertz. Applied Acoustics. 60() (000). 5. Feldman, E. J.Acoust.Soc.Am. 98(1) (1995). 6. T J Cox and P D Antonio. Applied Acoustics. 60() June 000. quadratic residue diffuser is shown. It shows that

6 Comparison between measurements of the scattering and diffusion coefficients A. Farina 1, L. Tronchin 1 IED, University of Parma, Parma, Italy DIENCA-CIARM, University of Bologna, Bologna, Italy In this paper the results of a wide comparative experiment are presented. 14 different small-sized scattering panels were tested making use of the new method based on the Wave Field Synthesis [1]. From the experimental raw results, with proper processing, both the scattering coefficient [] and the diffusion coefficient [3] can be derived. The octave-band spectra of these two coefficients are compared for each panel. As expected, it resulted that it is generally difficult to find a stable relationship between the two coefficients. The WFS method proved of consequence its value, being capable of yielding both coefficients from the same measurement results. On two panels, the measured values were cross-checked with other measurement methods. It resulted that the diffusion coefficient is almost the same as the value obtained by the AES-standard method, whilst the scattering coefficient is much less correlated with the value measured, on a large continuous surface, with the Mommertz/Vorlander method. This difference was explained considering that the WFS method is applied to a single panel, where border effects are predominant (particularly at low frequency), and these effects are instead minimized making use of a large continuous surface. DIFFUSION AND SCATTERING COEFFICIENTS The acoustical scattering properties of uneven surfaces are judged to be very important for proper numerical simulation of the sound propagation in enclosed spaces. Furthermore, many diffusing panels are on the market nowadays, and it is not easy for the acoustical designer to specify what kind of panels is optimal for a given case. There are no standardized measurement methods. Furthermore, two different approaches are followed by AES and ISO Committees, which are confusing in some way the meaning of diffusion and scattering properties. from which the scattering coefficient is obtained: E s = E spec tot αspec α = 1 α The direct and reflected sound can be simply obtained by time-windowing the IRs, as in the following figure tot tot THEORY:1 MOMMERTZ- VORLÄNDER METHODOLOGY The first method of measuring scattering was developed by Mommertz and Vorländer and it s called free-field scattering measurements method. The scattering coefficient is defined as: Ediff Ediff s = = E E + E tot therefore, after FFT post-processing of the measured IR (obtained rotating the panel at 5 steps in 7 angles), extracting the spectrum of reflected IR, for each frequency the absorption coefficient is: α tot FFT ( IRtot = 1 ; α FFT ( IR ref spec spec = 1 diff FFT ( IR FFT ( IR spec ref FIGURE 1. Time-windowing of direct and reflected sound THEORY: WAVE FIELD SYNTHESIS METHODOLOGY Since the scattered wavefronts have more curvature than the specularly reflected one, the WFS approach can easily separate the two wavefronts. The data acquisition setup consists of a soundfield microphone moving along a straight line instead of a hemicircumference. For each microphone position, the total diffused energy coming from the panel is calculated. b a W z ( α) = c 1 s loc I diff dx dy 3 y= b x= a 4 π r1 π r

7 whilst the specular reflected intensity coming from the panels and measured only in those positions of the microphone within the specular zone, is: W Ispec = 4 π ( 1 α) ( 1 s ) [( z z ) + x ] c r The estimation of ISO scattering coefficient is therefore obtained simply minimizing the difference between numerical calculations and experimental measurements. loc r From experimental data, polar plot were obtained. The spectra of both direct and reflected sound from numerical formulation were compared with measurements; absorption and scattering coefficient were obtained minimizing differences between numerical and experimental data, by meaning of a worksheet solver. The procedure was repeated for octave frequencies, from 15 to Hz Scattering Coefficients Scattering Co efficient (s) Frequencies absorb 0 absorb 45 absorb 90 FIGURE. Setup of the acoustical apparatus for the measurements with the Vorlander-mommertz free field method ANALYSIS AND RESULTS FROM MEASUREMENTS Different panels were analyzed, and the scattering coefficient was measured as reported. Specialized software was developed, and all the 55 IRs measured with WFS approach were fitted in only one waveform. Direct and reflected sound were separated by software, and analyzed. FIGURE 3. Polar plot: Whole IRs, (left) direct (center), reflected sound (right) FIGURE 4. Scattering coefficient for different angles on incident sound ACKNOWLEDGMENTS The authors whish to thank Michele Zanolin for his help during the acoustical measurements and subsequent data analysis. REFERENCES 1. A. Farina - "A new method for measuring the scattering coefficient and the diffusion coefficient of panels", Acustica/Acta Acustica, vol. 86, n. 6 pp , ISSN , December 000. E. Mommertz, M. Vorländer, "Measurement of scattering coefficients of surfaces in the reverberation chamber and in the free field" - Proc. 15th ICA, Trondheim, 1995, pp P. D Antonio, T. Cox, Two Decades of Sound Diffusor Design and Development, Part : Prediction, Measurement and Characterization Journal of AES vol. 46, n 1, pp (December 1998). 4. A. Farina, M. Zanolin, E.Crema Measurement of sound scattering properties of diffusing panels through the Wave Field Synthesis approach, Preprints of the 108th AES Convention, Paris, 19- February 000

8 Application of Scattering Surface in Absorber Design Y.W. Lam and T. Wu School of Acoustics and Electronic Engineering, University of Salford, Brindley Building, Meadow Road Site, Salford M7 9NU, UK. It has been known for some time that a Schroeder diffuser can provide unusually high absorption over a wide frequency band. This is due to the multiple resonances and the surface impedance discontinuity created by the different well depths in the diffuser. It has also been shown theoretically and verified by experiments that the absorption can be enhanced considerably by placing a resistive layer on the surface of the diffuser. This paper describes an exploitation of this absorption mechanism under an EC funded project, RANNTAC, to develop a honeycomb based absorber design. In the simplest form, a resistive facing sheet can be placed on top of a honeycomb cavity structure to provide a one degree-of-freedom resonant absorber. The honeycomb cavities can be modified by means of inserts to create well depth sequences that are similar to those of Schroeder diffusers to extend the frequency range of high absorption. The particular problems faced by this application were the very small size of the honeycomb cells (around and a depth of ), and the dimensional hexagonal arrangement of the cells. A computer model was developed to optimise the depth sequence to provide near zero reactance over a wide frequency band. Samples of the design were tested at normal and oblique incidences to verify the prediction. It was found that the design can extend significantly the frequency range of the absorber. The small reactance is well suited for room acoustic applications, and it is also possible to extend the low frequency performance by means of hollow inserts. INTRODUCTION Absorptive intake liners are one of the most important means for controlling aircraft noise. The design of conventional 1 degree-of-freedom (DOF) liners has been established for many years. However current and future demands on noise control require liner performances that are beyond the capability of conventional liners, and innovative techniques are being sought to significantly improve liner performance. The enhanced absorption provided by a scattering surface was first observed in studies on Schroeder diffusers, and particularly in the quadratic residue diffusers (QRDs). The reasons for this high absorption produced by variable depth scattering surfaces has been thoroughly investigated and prediction model was developed and verified against various configurations of QRD and similar scattering surfaces typical in audio applications [1]. This paper reports on a study to adapt this variable depth design into an intake liner. ABSORPTION MECHANISMS A schematic representation of the liner concept for a period N=7 design is shown in Figure 1. The increase in sound absorption comes from two mechanisms: Each cavity resonates at a different frequency from other cavities because of the different depths, giving a wide frequency band width of high absorption and a smooth frequency response. The differences in the wave responses between adjacent cavities increases energy flow between cavities. Therefore a resistive layer placed at the entrance to the cavities significantly increases the absorption (resistance). L b T Pe e z ADAPTATION TO LINER DESIGN The particular problems faced by this application are the very small size of the honeycomb cells, which means that boundary losses are significant, and the hexagonal arrangement of the cells. One of the biggest practical difficulty of the variable depth design is the creation of the different depth in the honeycomb cavities of a liner. In a typical liner there are thousands of cavities per m. Inserts were considered the most practical solution to create the different depth. In the original design, it was considered necessary to minimise potential gaps between the inserts and the honeycomb walls in order to eliminate unwanted acoustic effects. Hence hexagonal inserts with a crosssectional shape identical to the cavity cells was used. P w N-1 Figure 1 Variable depth scattering surface ln x

9 Unfortunately this also means that the fit between the inserts and the cavities is very tight and it is extremely difficult to put in the inserts without damaging the honeycombs. The problem is particularly severe for the large samples as there are thousands of inserts to put in. To reduce this construction difficulty, round cylindrical inserts were used to construct the 1mx1m sample. This created small gaps between the inserts and the cavity walls. Nevertheless investigations on the effect of perforation in cells suggested that these gaps are likely to improve rather than reduce absorption. The measured normal incidence impedance of a 1mx1m liner sample, which used the round inserts, and that of a small impedance tube sample, which used the hexagonal inserts, are compared together with prediction in Figure. Both samples are of typical liner dimensions. The depth sequence was identical in both samples, optimised to give minimum reactance over the frequency range of the design. Impedance Normal incident Frequency,Hz Prediction:R X Anechoic-room:R X Impedance-tube:R X Figure Impedance of a variable depth liner design. It can be seen that the two measured impedance spectra agree very well with each other and there are no obvious problems created by the use of the round inserts. It should be noted that the impedance tube measurement was limited to 3000Hz which is not high enough to cover the main operational frequency range of the design, which extends beyond 5000Hz. Nevertheless the 1mx1m sample measurement, which produced results up to 5000z, does agree fairly well with the prediction by the computer model, which assumed no gaps between the inserts and the cavity walls, up to about 3.5kHz. Importantly the imaginary part of the impedance (reactance) remains close to zero as designed at the higher frequencies. Since the variable depth sequence creates nonuniform impedance distribution on the surface that is theoretically dependent on the angle of incidence, oblique incidence measurements were also performed on the large 1mx1m sample in an anechoic chamber. The frequency trend of the impedance at up to 30 incidence, which was the limit of the measurement setup, remains similar to that at normal incidence and agrees well with prediction. ASSESSMENT OF PERFORMANCE A liner design with reactance optimised to stay close to zero over the frequency band of interest was submitted to our partners in the RANNTAC project for evaluation against engine noise reduction criteria. The evaluation result suggested that the final variable depth sequence design is good at low frequency and has a smooth/flat frequency spectrum. However it still has two significant drawbacks: a) the resistance value is generally too low, and b) the reactance values were optimised to near-zero values which is good for one flight condition but not for others. This is mainly due to the fact that the variable depth liner design used a linear resistive facing sheet and as a result could not match the different values of the optimum impedance required for different flight conditions. CONCLUSION The theoretical optimisation of the variable depth sequence liner concept was successfully verified by experimental tests on liner samples. The result of the optimisation process has produced a liner design that shows significant improvement over conventional liners at low frequencies and in the consistence (smoothness) of the mid to high frequency performance. However the current design only provides significant improvements in on flight condition and is worse than an optimised 1 DOF liner in the mid to high frequency range in other flight conditions. The poorer performance in these conditions is mainly due to the lower resistance value and the small reactance of the liner. The latter is a consequence of the optimisation process that was aimed to produce near-zero reactance values, and that the liner was designed to be linear and therefore impedance does not change with operation conditions. ACKNOWLEDGMENTS This work is funded by the EC Brite Euram project RANNTAC. Support from all partners in the project are kindly acknowledged. REFERENCES 1. T. Wu, T. J. Cox, Y. W. Lam, J.Acoust.Soc.Am. 108(), pp , 000.

10 Investigations on the ISO measurement method for scattering coefficient in the reverberation room Márcio H. A. Gomes a, b, Michael Vorländer a, Samir N. Y. Gerges b a Institute of Technical Acoustics, Technical University of Aachen, Germany - Templergraben Aachen Tel.: (041) /86 -E -mail: [email protected], [email protected] b Laboratory of Acoustics and Vibration, Federal University of Santa Catarina, Brazil The correlation method for measuring the scattering coefficient in a reverberation chamber is most likely to be internationally standardised in ISO. In this method the impulse response of a reverberation chamber is measured, first without and next with the sample placed with different orientations. As one sums these impulse responses, one gets as result an impulse response related to the specular reflection only, with a decay faster than compared with a single measured impulse response decay. From these results the scattering coefficient is determined. An ISO working group discusses and develops the referred method. Some questions still are to be answered, for instance, on the edge effects and the corresponding demands on scale factor and sample size. In this paper a preliminary investigation about the edge effects over the results and a comparison with results obtained with another method is reported. INTRODUCTION The correlation method for measuring the scattering coefficient [1] can be applied either in free or diffuse sound field. In the last years more attention was given to the application of the method in the diffuse field and an ISO working group prepares the release of a standard for measuring the scattering coefficient in the reverberation chamber. In the diffuse field only scattering coefficients due to random incidence are measured and the procedure is similar to the measurement of the random incidence absorption coefficient. Here an additional absorption coefficient related to the specular component of the reflection has to be determined. This is done by evaluating the reverberation time calculated from averaged impulse responses measured with the sample oriented in a sufficient number of different orientations (completing one rotation). As the scattered components of the reflection are cancelled out, the resulting impulse response contains only information about the specular component of the reflection. The absorption coefficient and the specular absorption coefficient are then calculated through the following relations: α s = 55,3 V cs α spsec = 55,3 V cs 1 T T4 T 3 1 T (1) () Here T and T 1 are the reverberation times measured in the chamber with and without the sample, respectively. T 4 and T 3 correspond to the reverberation times obtained from the averaged impulse responses, again with and without the sample. The scattering coefficient is calculated through the relation: αspec αs s = (3) 1 α s Some aspects of this method are under investigation, such as the influence of edge effects and air absorption on the results (since it is usual to perform the measurements in scale models). Next a first investigation related to the influence of edge effects will be briefly addressed. The results of a measurement performed with this method and those obtained from a method which may be standardised by the Audio Engineering Society (AES), a free field measurement, were also compared through the application of the Paris formula []. Edge effects When measuring the scattering coefficient in the reverberation chamber, the set-up consists of sound source, receiver and a round base plate placed over a turn table. For practical reasons the samples are constructed sometimes over a square plate. It is known, however, that the square plate itself scatters the incident sound. Three measurements were performed in order to have an idea of how this additional scattering affects the results and if this effect can be corrected. First the scattering coefficients of small hemispheres randomly spread over a square area were measured (directly over the round base plate). The same was performed, but now with the hemispheres spread over a square plate (60 x 60 x 1,6 cm, placed over the round base plate). Finally, the

11 Scattering coefficient scattering coefficients of the square plate alone were measured. The results are shown in Fig. 1. 1,0 0,9 0,8 0,7 0,6 0,5 0,4 0,3 0, 0,1 0,0 hemispheres over a square plate hemispheres over a square area square plate 0,16 0,0 0,5 0,30 0,40 0,50 0,63 0,80 1,00 1,6 1,60,00 a/λ FIGURE 1. Scattering coefficients from hemispheres spread over a square area, hemispheres spread over a square plate and only the square plate. a is the average distance between the hemispheres (5,4 cm) and λ, the wave length of sound in air (0 C). The scattering from the square plate self can significantly influence the results and its scattering coefficients are excessively high above a/λ = 0,63. An attempt to correct the results was done, considering the set-up to contain also the square plate over the round base plate. This is equivalent to substitute T 1 and T 3 in the measurement of the hemispheres spread over the square plate by T and T 4 obtained in the measurement of the square plate alone. The corrected results are shown in Fig., compared with the results for the hemispheres spread over the square area (without the square plate). The correction works well, in this case, up to a/λ = 0,80, but above this frequency the difference between corrected results and the measurement performed with the hemispheres spread over the square area are larger than expected. Comparison with other methods A sample from the RPG Flutter Free diffuser was measured by the RPG with the AES method (in the free field) and the results were compared to those obtained using the correlation technique in the diffuse field. At RPG the scattering coefficient was measured for three angles of incidence (0, 30 and 60 degrees). In order to correct these values for random incidence, the Paris formula [] was used (see Figure 3). The discrepancies at lower frequencies are probably related to the influence of the edges. At middle and higher frequencies the errors may be also related to the fact that the measurements in the free field were performed only for three angles of incidence. To have a better approximation for the random incidence scattering coefficient, it is necessary to have more terms weighted by the Paris formula. The general aspect of the comparison, however, is considered satisfactory. Scattering coefficient FIGURE. Correction attempt for the influence of the square plate over the measurements of the scattering coefficient. Scattering coefficient 1,0 0,9 0,8 0,7 0,6 0,5 0,4 0,3 0, 0,1 0,0 1,1 1,0 0,9 0,8 0,7 0,6 0,5 0,4 0,3 0, 0,1 0,0 hemispheres over a square area correction attempt 0,16 0,0 0,5 0,30 0,40 0,50 0,63 0,80 1,00 1,6 1,60,00 a/λ ITA - correlation technique RPG - AES technique - Paris 0,0 0,5 0,35 0,40 0,50 0,70 0,85 1,00 1,30 1,70,10,60 a/λ FIGURE 3. Comparison between the scattering coefficients of a RPG Flutter Free diffuser, measured with the ISO correlation technique in the diffuse field and the AES technique in the free field. a is the length of one profile of the Flutter Free. The topics here discussed are objects of current research. Useful results are expected from numerical calculations of the scattering coefficient of simple surfaces and further comparisons with measurements performed in other laboratories. ACKNOWLEDGEMENTS The authors would like to kindly acknowledge Janina Fels, Dr. Peter D Antonio and Dr. Trevor Cox for the data sent from RPG. REFERENCES 1. Vorländer, M.., Mommertz, E. Applied Acoustics 60, (000).. Kuttruff, H., Room Acoustics, Spon Press 000, pg. 49.

12 A Standard Method for Assessing Diffusor Quality P. D Antonio a, T. J. Cox b a RPG Diffusor Systems Inc., 651-C Commerce Drive, Upper Marlboro, MD 0774, USA. b School of Acoustics and Electronic Engineering, University of Salford, Salford, UK. One of the challenges in room acoustics is to develop diffusing surfaces that complement contemporary architecture in the way that statuary, columns and relief ornamentation complemented classic architecture. A key element to enable holistic diffusor design is a diffusion coefficient to enable the evaluation of surface scattering. The diffusion coefficients developed have facilitated design via numerical optimisation. This has enabled the palette of surfaces with defined acoustic performance to be expanded. The diffusion coefficient is a measure of the uniformity of the free field scattered polar distribution. The polar responses can be readily measured using MLS techniques or predicted using boundary element methods. An autocorrelation approach tests the spatial similarity of the polar distributions. This autocorrelation approach is summarised in a simple equation that enables the diffusion coefficient to be readily calculated. The method has recently been published in an Audio Engineering Society standard information document AES-4id-001, which summarises the findings of the working group sc In this paper, the rationale behind the diffusion coefficient standard will be given. The use of the coefficient in diffusor design and the role it plays in performance specifications will be reviewed. INTRODUCTION It is understood that surface diffusion can play an important part in determining the sound quality of many rooms. The surface diffusion may come from incidental features of the room such as statuary, columns and relief ornamentation, or from especially designed diffusors. Whether diffusion comes by design or not, it is important to evaluate the diffusivity of the reflections, to better understand the role of diffusion in room acoustics. Working under the auspices of the Audio Engineering Society, the authors have been chair and vice chair of working group sc-04-0, which has been developing standard methods for evaluating the diffusivity of reflections. This has culminated in a standard information document [1] being published earlier this year detailing a method. This paper intends to outline the rationale behind AES-4id-001, and to shown how it can be used in diffusor design and performance specifications. DIFFUSION COEFFICIENT The test surfaces are evaluated in terms of their ability to disperse sound energy uniformly over a polar response, whether this is measured in a single plane or over a whole hemisphere. It is assumed that complete diffusion occurs when every measurement position on the polar response receives the same scattered energy. Examples of measured polar balloons are shown in Figure 1, which shows that the skyline is better at Figure 1. Measured 3D Polar balloons. Left.5kHz, skyline, normal incidence. Right 1.5kHz, random battens, 60º incident sound. diffusing the reflected sound. The standard information document details measurement methods requirements for getting these polar distributions. The most straightforward method is to use a maximum length sequence system and time gating to extract the scattered energy. Measurement in a single plane is relatively straightforward, full 3D measurements are more logistically difficult. Alternatively, prediction models can be used - it is well established that Boundary Element Methods (BEMs) give remarkable prediction accuracy. Within this evaluation philosophy, lie some of the method s weaknesses and strengths. The concept of measuring the smoothness of energy polar distributions is straightforward. Yet, the issue of wavefront phase is not considered. A single cylinder spatially disperses energy very efficiently, but does this without dispersing the phase. (There is anecdotal subjective evidence that cylinders are not good diffusers for this reason). The other problem is that the

13 polar distribution must be measured in the far field, and this extends a very long way for large surfaces. Once the polar distribution is obtained, it is reduced to a single figure of merit. This is done using the circular autocorrelation function, which measures the spatial similarity in the energy polar distribution. An exhaustive test of many different surface types [] showed that this was the best coefficient available. What could potentially be a complex calculation procedure, fortunately reduces to a simple equation. The diffusion coefficient, d, is given by: d n i1 E i n / n E (1) i1 i Where E i s are the n energies in the polar distribution (an even area sampling is assumed here). d is automatically bounded between 1/n (specular reflection) and 1 (uniform diffusion). A simple scaling can be done to make the bounding between 0 and 1. Figure. Diffusers designed using optimisation APPLICATIONS Acoustic designers are used to specifying the required absorption coefficient of surfaces in room designs. Yet, diffusion is often applied in a more haphazard fashion, with no quantification of whether too little, or too much surface diffusion is being using. By creating a standard evaluation technique, it is hoped that a more scientific basis for the application of surface diffusion can be formed. For example, the technique outline here is already being used as the basis of performance specifications for auditoria and other performance spaces. This diffusion coefficient has also influenced the design of diffusers. Very few surface types have simple design equations; exceptions are Schroeder diffusers and some simple concave arcs. Problems then arise if these diffuser designs are visually unappealing to the architect. Consequently, an optimisation has to be used to enable a design that is both visually appealing and meets acoustic requirements. In optimisation, an iterative search is undertaken to look for the best diffusor. For example, it is possible to task a computer to find a well depth sequence that give better performance than the quadratic residue sequence. During the trial and error process, the computer predicts polar responses from the surface, and then reduces the polar responses to a single figure of merit the cost parameter. The figure of merit used is the autocorrelation diffusion coefficient. This not only enables better depth sequences to be obtained, it also makes it possible to make designs or arbitrary shape. The only restriction is that the shape must be mathematically definable with a few shape parameters, and the polar response must be predictable. Figure (top) shows an example of a curved optimised surface designed to reduce the focussing effect of a concave wall. Figure (bottom) shows a stage canopy also designed using optimisation and the autocorrelation diffusion coefficient. CONCLUSIONS AES-4id-001 sets out a diffusion coefficient which ranks the performance of diffusers correctly and is intended to evaluate diffuser quality. It is not perfect, but even the absorption coefficient has flaws. By ensuring that diffusers are tested against this standard, a better understanding of the role of diffusion in rooms can be developed, as well as ensuring that diffusers perform up to quantitative specifications. REFERENCES 1. AES-4id-001. AES Information document for room acoustics and sound reinforcement systems Characterization and measurement of surface scattering uniformity J.Audio.Eng.Soc. 49(3) (001).. T J Hargreaves, T J Cox, Y W Lam and P D'Antonio. J.Acoust.Soc.Am. 108 (4), (000).

14 Determination of the Scattering Coefficient of Statistical Rough Surfaces J.J. Embrechts Department of Sound and Image Techniques, University of Liège, Sart-Tilman B8, B-4000 Liège 1, Belgium, [email protected] Abstract : The scattering coefficient of a diffusing surface accounts for the part of sound power which is non-specularly reflected. This coefficient is an essential parameter for the description of walls and surfaces in room acoustics problems. In this paper, the scattering coefficient of random rough surfaces is calculated from the complete scattered sound pressure distribution. This distribution is evaluated using a Kirchhoff Approximation method. The results obtained for several rough surfaces are compared with theoretical expressions of the scattering coefficient. These expressions show the influence of the angle of incidence, the sound frequency and the geometrical parameters of the surface profile on the scattering coefficient. It is shown that these theoretical expressions give reliable results as long as the Kirchhoff Approximation conditions hold. INTRODUCTION In room acoustics, the scattering coefficient of a diffusing surface is defined as the ratio of nonspecularly reflected power to the total power reflected by the surface. The value of this coefficient (and its dependence on frequency) is essential for the users of any modern room acoustics software, because most of them can now account for the effects of surface diffusion. However, rather few data have already been collected on surface scattering properties and only a small part of these data have been published. Therefore, a great amount of work must still be done in order to better understand the mechanisms of surface scattering and to measure diffusion parameters. The random-incidence scattering coefficient of diffusing surfaces can be measured in a reverberant room, using a method developed by Vorlaender and Mommertz [1]. This method is presently under investigation by an ISO working group. However, this communication addresses the problem of finding the value of the scattering coefficient, not by measurements, but rather by theoretical developments. METHOD SUMMARY We consider finite size rough surfaces described by their elevation z = ξ ( x, y) relative to a reference plane. Assuming an incident plane wave, the distribution of the scattered pressure can be calculated with the Kirchhoff Approximation method []. The development of this method leads to the following expression for the complex pressure p 1 in the scattering direction k s : p1( ks ) = K e S jv. r ( v. γ ) C r dx dy In this equation, K is a constant complex number (depending on the strength of the incident wave and the distance of the receiver), S is the area of the rough surface projected onto the reference plane, v = k i k s where ki is the incident vector (the magnitude of both vectors k is π / λ ), r is the position vector of the surface element at ( x, y, ξ ) and ' ' γ = ( ξ x, ξ y,1) is a vector perpendicular to the rough surface at this surface element. Cr is the local reflection factor. With this expression, it is possible to calculate (within the assumptions of the Kirchhoff Approximation which are not discussed here) the complete distribution of the complex scattered pressure. The scattering coefficient of the diffusing surface defined by z = ξ ( x, y) can then be obtained with a formula proposed by Mommertz [3]. This scattering coefficient is called in the following δ K.A., since it is computed using the more general formulation of the Kirchhoff Approximation method. (1)

15 RESULTS FOR GAUSSIAN ROUGH SURFACES To solve (1), we of course need to define the profile of a given rough surface. In this study, the analysis has been focused on a typical class of random rough surfaces, namely the gaussian surfaces. For these particular surfaces, it is possible to derive fairly good approximations of the scattering coefficient δ K.A.. As will be seen in the following, these approximations can be obtained without calculating the complete distribution of the scattered pressure. They are therefore more easily computed and they also better illustrate the influences of sound frequency and geometrical parameters on the scattering coefficient. The first approximation is : 1 δ C. F. = 1 rs rs = e S S jvz ξ dxdy () where C.F. means characteristic function, which is the jv mathematical name for the average of z ξ e if ξ is a random variable. The second approximation is : δ RMS 4s k cos θ 1 i = 1 e s = S ξ S ( x, y) dxdy In this expression, θ i is the angle of incidence of the plane wave and s is the r.m.s. height of the random rough surface. Both approximations have been compared with the theoretically exact value of the scattering coefficient δ K.A. derived from equation (1). The characteristic function model () always leads to a very good correlation with δ K.A., as long as the conditions of validity of the Kirchhoff Approximation are satisfied. The rms height model (3) states that the scattering coefficient of gaussian rough surfaces only depends on the r.m.s. height of the surface (relative to the wavelength) and on the angle of incidence. The correlation with δ K.A. is not as good as in the previous model, but the deviations are not really significant unless the scattering coefficient reaches high values (δ>0.8). This is illustrated for a particular class of gaussian surfaces in figure 1. (3) interpretation of the influence of all parameters affecting the scattering coefficient. Scattering coefficient FIGURE 1. Scattering coefficients δ K.A. and δ RMS computed from expression (1) and by the rms height model (3) respectively, for 00 rigid ( C r = 1) gaussian rough surfaces characterized by a correlation length of 5λ. The angle of incidence is 0. Figure 1 gives only some examples of the many gaussian surfaces which have been considered in this study. After analysing all these results, it has been found that the approximations () and (3) are in fact valid in many situations, including many angles of incidence ( θ i 60 ), surface dimensions, correlation lengths ( T λ ) and r.m.s. heights. We even found that the approximations also hold for non-rigid surfaces. It turns out that, at least for gaussian rough surfaces, the key parameters (concerning sound diffusion) seem to be the ratio of r.m.s. height to the wavelength and the angle of incidence. Further similar studies on other surfaces with deterministic profiles will certainly bring new information to this theory. REFERENCES delta K.A. delta RMS r.m.s. height relative to wavelength s/lambda 1. Vorlaender, M., and Mommertz, E., Applied Acoustics, 60, (000).. Thorsos, E.I., J. Acoust. Soc. Am., 83(1), 78-9 (1988). 3. Mommertz, E., Applied Acoustics, 60, (000). On the other hand, the rms height model is much easier to calculate, and it gives a very clear

16 Studies of Scattering from Faceted Room Surfaces R. R. Torres a, M. Vorländer b, U. P. Svensson c, and M. Kleiner d a Program in Architectural Acoustics, Rensselaer Polytechnic Institute, 110 8th St., Troy, NY 1180, USA b Institute of Technical Acoustics, Technical University Aachen, D-5056 Aachen, Germany c Acoustics Group, Dept. of Telecommunications, Norwegian Inst. of Technology, NO-7491 Trondheim, Norway d Chalmers Room Acoustics Group, Chalmers Univ. of Tech., SE Gothenburg, Sweden To improve room acoustics modeling and design, studies of edge diffraction and scattering are performed. Examples of room components where modeling of edge diffraction is important include reflector panel arrays, grazing incidence over seats, orchestra pits, and other surfaces whose dimensions are comparable to or less than the wavelength of interest. Here, scalemodel measurements of edge diffraction are performed to illustrate that complex diffraction interferences cannot be accurately modeled with simple, energy-based Lambert models of diffusion. Hence, the natural spectral coloration in the early impulse response would be likewise inaccurately represented in numerical simulations and auralization. INTRODUCTION The scattering behavior of faceted and rough surfaces is of particular importance in room acoustics, as it determines the spatial coverage and spectral coloration of early reflections to listeners. In this paper, the behavior of faceted surfaces is investigated. MEASUREMENTS Previous studies modeled edge diffraction from a stage house, considered as an assemblage of wedges [1-3]. For increased understanding, we study here the scattering from a small number of facets. A common example in architectural acoustics is the use of overhead reflector arrays to optimize the delay times, strengths, and frequency spectra of early reflections in the room impulse response (RIR). We first measure the scattering from various arrays composed of 1 to 35 facets (i.e., panels). Figure 1 depicts a square-panel array (or, alternatively, long rectangular panels). We examine the effect of the array density on the reflected component and the dependence of the specular zone on frequency. The source is an 11.5-cm dodecahedron loudspeaker emitting maximum-length sequences (MLS), which have advantages over spark sources. The source and microphone are 50 cm below the array. Measurements on reflector arrays for room acoustics have been documented sporadically during the past few decades. One of the earliest systematic studies was performed by Leonard et al. [4], who measured the sound pressure at the receiver and compared it with that obtained for spherical sound spreading. They discussed frequency ranges where the reflection coefficient was negative and also confirmed intuitive predictions of the diffraction behavior at the low- and high-frequency limits. The work here studies spectral changes in the scattering and examines its spatial spread relative to the specular reflection zone. A1 A A3 A4 A5 C.L. G1 G G3 G4 G5 85 cm FIGURE 1. Example square-panel array. The solid circle is the source; the open circle, the microphone. RESULTS One interesting part of this study is the spreading of the energy around the geometrical, specular reflection zone (the middle region in Fig. ). The wavelengths for the octave bands (500-4 khz) in Fig. are similar to or greater than the panel widths (1 cm). Figure plots the normalized (for spherical spreading), squared amplitude of the scattering from a rectangular panel (top) and from a row of seven square panels. In the top figure, the scattering for the 1 and khz bands peaks when the incidence angle to the panel is closer to normal (greater projected panel area) and the specular reflection point is within 1/4 to 1/ wavelength of the

17 edge. Here the scattering depends more on incidence angle and projected reflecting area, and the specular zone seems to be less meaningful. approximations (such as Lambert s Law), which would possibly result in lower accuracy simulations. NUMERICAL MODELING Parameter studies are in progress, where edge diffractions from facets are computed using a model by Svensson et al. [], based on the Biot-Tolstoy and Medwin (BTM) approach [3]. The edges are divided into sources with analytically derived strengths. One sample of the impulse response h is then (Eq. 35, []): hi 4,, S, ml R, z (1) z is the length of the source at z i along the where edge, describes the wedge angle, m and l are source and receiver distances, and is an analytical edgesource directivity-function. Although the model has been validated for several cases, one must examine how it is best applied to more complex faceted surfaces. For example, when several separate facets lie in the same plane, certain propagation paths between edges would theoretically undergo second or thirdorder diffraction. Computing all of these paths may not be necessary to achieve a desirable degree of accuracy. ACKNOWLEDGEMENTS The authors thank Nikitas Gianni, Stefan Goertz, and the workshop of the Institute of Technical Acoustics for their assistance. FIGURE. Scattering from rectangular panel and multiple square panels. The specular zone is the middle third. Inter-panel interferences seem to lower the relative reflected amplitude of the 4 khz band. Second, in the lower figure, it is interesting that the reflected amplitude of the 4-kHz band no longer dominates over the -khz band, although one might expect that higher frequencies are reflected much more effectively, especially near the specular zone (as it is for the rectangular panel). At 4 khz, however, the wavelength is on the order of the panel width and separation, which allows inter-panel interferences that may cause the total reflected amplitude to decrease. Perceptually, this may change the perceived coloration because the spectral content of this reflection changes. This could be investigated in future subjective studies. One may note [5] that interference effects such as these (on the order of 5 db here) are not modeled explicitly by energy-based scattering REFERENCES 1. R. R. Torres, U. P. Svensson, M. Kleiner, Computation of edge diffraction for more accurate room acoustics auralization J. Acoust. Soc. Am. 109, (001).. U. P. Svensson et al., An analytic secondary source model of edge diffraction impulse responses, J. Acoust. Soc. Am. 106, (1999). 3. H. Medwin, Shadowing by finite noise barriers, J. Acoust. Soc. Am. 69, (1981). 4. R.W. Leonard et al., Diffraction of sound by an array of rectangular reflective panels, J. Acoust. Soc. Am. 36(1), (1964). 5. R. R. Torres, M. Kleiner, B.-I. Dalenbäck, Audibility of diffusion in room acoustics auralization: an initial investigation, Acustica (Special Issue on Room Acoustics) 86(6), (000).

18 Boundary Element Analysis as a Design Tool for Panel Arrays T. E. Gulsrud Kirkegaard Associates, Consultants in Architectural Acoustics, 954 Pearl Street, Boulder, Colorado, USA The boundary element method (BEM) is an established computational technique for engineering problems involving acoustic scattering and radiation. We discuss the application of the BEM to a frequently encountered design problem in room acoustics: scattering from arrays of panels suspended over a concert platform. The BEM is based on wave theory and does not depend on high frequency or far-field approximations, enabling it to predict low frequency scattering for a variety of source and receiver positions that ray tracing and other techniques cannot. We present a series of graphics to demonstrate the capability of the BEM to provide useful information to the designer of a panel array and offer some insight into the trends encountered in the data. The computations do not require a high performance workstation, placing this information within the grasp of the owner of a modest desktop or laptop computer. INTRODUCTION A panel array is frequently provided for music performance or rehearsal spaces when other architecture in the room is not able to provide early sound reflections to audience members or between musicians. While conventional ray tracing or other approximate methods [1] are available to the designer, these methods are limited by high frequency or farfield approximations. The boundary element method (BEM) permits low frequency reflections (wavelengths comparable to the dimensions of the panels) to be studied without restrictions on source or receiver locations. Calculation Technique The calculations are based on numerical solutions of the Helmholtz Integral Equation with the assumption of thin rigid panels, the development and validation of which can be found elsewhere [,3]. The resulting surface integrals are approximated by subdividing the reflecting surfaces into N elements and setting the value of surface pressures constant across each element. The surface elements must be smaller than ¼ the wavelength of interest in order to accurately model sound waves across the surface. The resulting set of simultaneous equations are solved in two steps. The equations are first solved for p j, the pressure difference across the panel at element j, due to the presence of a point source located below the panel array. This solution is then used to calculate the total scattered pressure p s from the panel array according to where k is the wavenumber of the source, x i is the receiver location, R ij is the vector from element j to x i, n j is a unit vector normal to element j, and A j the area of element j. The resulting total scattered pressure is referenced to the pressure from an image source, p i (x i ), above the panel array. The result is L, the level change in reflection due to the panel array compared to a reflection from a solid plane [1]. 10 p s ( x i ). 10 ( ) L = Log p i x i () Any variation from zero in L indicates the presence of diffraction from the finite size of the panels or interference from scattering from multiple panels. EXAMPLES To demonstrate the technique we present a series of calculation results for a sample 5x4 array of 6ft square panels illustrated in Figure 1. The on-center spacing of the panels is 8ft in both directions and the source is located 17ft below the center of the array. N 1 e p xi) = p 4π ikrij S ( j j= 1 Rij (1 ikr )( Rˆ ij ij nˆ ) A, j j (1) FIGURE 1. Plan view of the sample panel array. Array is located 0ft above the floor. The source is at (0,0,3)ft.

19 FIGURE. Distribution of L across a grid located 3.1ft above the floor. The resolution is 1 point per 0.5ft. Effect of Source Frequency Plots on the left side of Figure show the change in coverage pattern of the array with source frequency. Even at 15Hz (λ ~ 9ft) considerable energy is scattered from the array of 6ft panels. At 50Hz (λ ~ 4.5ft) scattering from individual panels and the resulting interference pattern is apparent. Results from a larger parameter study indicate that interference between waves scattered from individual panels cause dips in the steady-state frequency response of the panel array [4]. Effect of Panel Size Plots on the right side of Figure show the effect of panel size, maintaining the panel spacing in Figure 1 and the source frequency at 50Hz. Decreasing the panel size by only 0.5ft increases the depth of interference minima in the coverage pattern and introduces a new dip at the source position. Larger panels provide a smoother coverage pattern but still cause a dip around the source position. CONCLUSIONS Parameters within the designer s control can significantly change the coverage pattern of the array, and the BEM allows the designer to evaluate a variety of panel sizes, shapes, and orientations. The method is limited primarily by the large number of elements (and computer memory) required for very large arrays or high frequencies. Further work is required to evaluate whether the diffraction patterns shown in Figure are audible when the direct sound and reflections from all room surfaces are taken into account. REFERENCES 1. Rindel, J.H., Applied Acoustics 34, 7-17, (1991).. Cox, T.J., and Lam, Y.W., Applied Acoustics 40, , (1993). 3. Terai, T., J. Sound and Vibration 69, , (1980). 4. Gulsrud, T.E., Acoustical Properties of Hanging Panel Arrays in Performance Spaces, M.Sc. thesis, Dept. of Physics, Univ. of Colorado, (1999).

20 Shape and Diffusion in the Design of Music Spaces R. J. Orlowski Arup Acoustics, St Giles Hall, Pound Hill, Cambridge CB3 0AE, UK The design of diffusers based on boundary element methods has enabled much greater freedom in the geometrical design of music spaces whilst providing precise diffusion requirements. An example is presented of the design of a small recital hall which has used this technique. INTRODUCTION We are well aware that heavy ornamentation in nineteenth century concert halls gives rise to a high degree of sound diffusion and that this is evidently beneficial for providing good acoustic quality. The reduction of ornamentation in twentieth century architecture has led to other geometries and devices being used to provide diffusion. However, design of these various diffusing elements has had only tenuous connections with the theory of sound scattering. Design guidelines typically recommend that diffusing elements should protrude between 300 mm and 600 mm or alternatively that they should be convexly curved in plan and section. This rather general approach was dramatically changed when Schroeder proposed a method for providing sound diffusion using mathematical number theory sequences [1]. The idea was quickly taken up by Marshall and Hyde who installed Schroeder-type diffusers, based on a quadratic residue sequence, in the new Michael Fowler Centre concert hall in Wellington, New Zealand. constraints of Schroeder diffusers to provide a much greater range of stepped and curved diffuser shapes. Using numerical optimisation techniques and prediction methods, an architect or designer can select a desired shape or motif and this can be tailored to provide a diffuser with the required diffusion. This technique has been applied by Arup Acoustics to the design of a new recital hall, the Edwina Palmer Hall, for the Benslow Music Trust near London. For architectural reasons, a concave form was developed for the hall which obviously gave rise to concerns about focusing. Curve-shape optimisation was used to minimise focussing by the concave wall using a geometrical motif based on an amplitude modulated wave; the concave wall and optimised curve are shown in Figure 1. A comparison of the sound scattering by the optimised surfaces is shown in Figure. The acoustic result appeared to be successful and many installations followed in concert halls and also in recording studios. However, Schroeder diffusers have not become universally popular because their aesthetic, which generally consists of a series of parallel slots of different depths, does not particularly appeal to architects and designers of auditoria. A NEW APPROACH Research by Cox and D Antonio [] has produced accurate prediction methods for scattering from diffusers based on boundary element methods. This has enabled diffuser design to break away from the FIGURE 1. Concave wall and optimised amplitude modulated diffuser The optimised wavy wall satisfied the architect s design intentions as well as meeting the acoustician s requirement to neutralise focusing and provide diffusion. Figure 3 shows a plan of the rehearsal hall

21 and Figure 4 shows a view of the diffusing wall in the completed hall. produced an expansive sound with a very good balance between clarity and reverberance. Both musicians found the hall easy to play in. Objective measurements relating to diffusion will be presented in the spoken version of this paper. The success of the Benslow project has led Arup Acoustics to consider the curve optimisation technique for providing diffusion for other projects. Currently, designs are being developed where the modulations of the walls occur in both vertical and horizontal planes. FIGURE. Comparison of sound scattering at khz by optimised and concave surfaces with source on axis and receiver at focal point The wall was formed from 5 mm thick medium density fibreboard (MDF) with a paint finish although glass reinforced gypsum (GRG) was considered as an alternative material. It can be seen from Figure 4 that the wall steps back at high level. Also, thin vertical strips have been added to the curved surface. Both these changes to the optimised curve were implemented by the architect to enhance the visual aspects of the wall in the context of the overall space. Neither is considered to have a significant effect on the overall scattering performance of the wall. FIGURE 4. View of diffusing wall in completed hall ACKNOWLEDGMENTS Thanks are due to the Benslow Music Trust for allowing reference to their building design, and to RPG Diffuser Systems Inc who collaborated on the project. The Institute of Acoustics is acknowledged for permitting the reproduction of excerpts from Acoustics Bulletin. REFERENCES FIGURE 3. Plan of Rehearsal Hall Subjective listening tests to piano and clarinet music in the hall indicated a very uniform sound field with no evidence of focusing. Furthermore both instruments 1. M. R. Schroeder, J. Acoust. Soc. Am. 57, (1975). P. D Antonio and T. Cox, J. Audio Eng, Soc. 46 (11), (1998)

22 A Method of Evaluating Surface Diffusivity of Rooms Using a Rectangular Scale Model C. H. Haan a and T. J. Cox b a Department of Architectural Engineering, Chungbuk National University, Chongju, , Korea b School of Acoustics and Electronic Engineering, University of Salford M5 4WT, UK The present study aims to express a new insitu method to measure the global diffusivity of surfaces in rooms. The present study verifies the results of the previous investigations using computer modeling and field measurements. The new criterion ( x) of surface diffusivity is the difference in the room acoustical parameters between two microphones of which the first microphone (M1) is facing the stage while the other microphone (M) is facing the rear wall of the room. The experiments were undertaken using a rectangular scale model with different surface diffusivity conditions. SPL, EDT, C80, were measured at six measurement positions and the x of acoustic parameters calculated and analyzed. The results show that the difference in the acoustic parameters in a room with high surface diffusion, is smaller than the difference in a room with little surface diffusion. This was true at every frequency and every position measured. METHOD OF EVALUATING SURFACE DIFFUSIVITY A new method of evaluating global surface diffusivity of rooms was introduced using computer modeling and field measurements [1,]. This was done by a pair of microphones, one microphone facing the front and one the rear wall of room respectively. A specially designed microphone holder panel is used to shadow the microphones appropriately. If the sound level at one position can be measured, eliminating the direct sound and early specular reflections, the amount of diffused sound could be predicted by comparing it with the value of sound levels in a non-diffused condition. This could be applied to any other acoustic parameters, so that we may know how much diffused sound affects the value of acoustic parameters. In this way, it can be shown that the difference of acoustic parameters at one position is depend on the surface condition of room. The value of acoustic parameters at the first microphone (M1), facing the front of room, is normally expected to be larger than the value of the second microphone (M), facing the rear wall of room. This occurs because M cannot capture the direct sound. The difference in the values between the two microphones changes depending on the surface diffusivity. The more diffusing elements on walls and ceiling the more sound that reaches M compared to a room with no diffusing elements. It is expected that the difference of values between two microphones will get smaller depend on the surface diffusivity of room. Therefore, an evaluation criterion, x, of surface diffusivity was suggested as follows: x = x (M1 ) x (M ). Where, x(m1) is the value of acoustic parameter obtained from microphone facing the stage of hall and x(m) is the value of acoustic parameter obtained from microphone facing the rear wall of hall. SCALE MODEL EXPERIMENT In order to investigate the effect of surface diffusivity on the acoustics of rooms, two different surface conditions were employed to make different surface diffusivity in the scale model. The surface condition of scale models was changed using and 3-dimensional diffusers including quadratic residue and primitive root diffusers. The diffusers were installed on the both sidewalls. The floor and rear wall was covered with pyrosorb foam to simulate absorptive areas typically found in real halls. The rectangular scale model had dimensions of 3.5 m length, m width and average height of.0m. A sound source was located at the center of the stage and six measurement positions were selected in the scale mode. 1/10 scaled omni directional speaker was used to radiate MLS signals five times at each measurement. In the scale model experiment, a microphone holder panel was employed to measure the x. There are two holes for insertion of microphones. The diameter of the microphone holder panel is 0 cm which is correspond with the wave length of 1700 Hz.

23 The effect of the microphone holder panel on the frequency range was investigated in an anechoic chamber changing the angle of incident sound to the panel by every 30 degree. Through the FFT analysis, it was detected that diffractions occur around Hz depending on the angle of incident. The microphone holder panel was installed at each measurement position 1cm above the floor. The measurements of acoustic parameters were undertaken using two microphones at the same time in order to enhance the reliability of the measurements. RESULTS Measurements were undertaken for acoustic measures such as sound level (SPL), early decay time (EDT), clarity index (C 80 ) at each measurement position. Also, the difference of acoustic values between two microphones was calculated and analyzed for both frequencies and measurement position. Fig.1 shows the average difference of sound level ( SPL) obtained from two microphones at each surface diffusivity conditions. The values below 000 Hz were eliminated due to the diffraction caused by the size of the microphone holder panel. Fig.1 represent that SPL of diffused room (D) and is smaller than that of nondiffused (N-D) room. This means that more sound reflections arrive at the receiving position in late sound field as well as in early sound field in the hall with high surface diffusivity. ÄSPL (db Frequency (KHz) Figure 1. Average difference of sound level (SPL) versus frequency for each diffuse condition. Also, the average differences of sound level, SPL, of each receiver position are illustrated in Fig. in order to show the difference of acoustic values depend on the position. Fig. shows that the smaller difference of SPL is evenly distributed in the room of high surface diffusivity regardless of the positions. In the same way, the difference of clarity index and early decay time were analyzed. Fig.3 shows the average difference of clarity index ( C 80 ) between two microphones for each diffuse condition. The figure N-D D displayed same result as shown in Fig.. The difference of C 80 of room D is smaller than that of room N-D at every octave band above 000Hz. ÄSPL (d r1 r r3 r4 r5 r6 M easurem entposition N-D Figure. Difference of sound level (SPL) of each measurement position. ÄC (db k 3.1k 4.0k 5.0k 6.3k 8.0k Frequency (Hz) D N-D Figure 3. Average difference of clarity index (C 80 ) versus frequency for each diffuse condition. DISCUSSION AND CONCLUSION The results from the present paper confirm the previous findings from the computer modeling and field measurements. It must be mentioned that there are some needs to know the objective scale of the measured values in order to evaluate the surface diffusivity of room. However, it was clearly shown that the difference of acoustic parameters, x, works well as a possible criterion of evaluating the surface diffusivity of room. ACKNOWLEDGEMENT The present work was supported by the Korea Research Foundation Grant (KRF-000-A0148). REFERENCES 1. C.H. Haan, and. K.W. Kwon., Applied Acoustics, to be published, (001).. C.H.Haan, Proc. of Institute of Acoustics Conference, Liverpool, (000). D

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26 Influence of Different Kind of Diffusers on the Degree of Diffusion of a Room J Redondo, J. Ramis, J. Alba Departmento de Física Aplicada, Escuela Politécnica Superior de Gandía, Universidad Politécnica de Valencia Carretera Nazaret-Oliva, SN Gandía, Spain The last years have been devoted to study how diffuse reflections affect sound. However, at this moment, there is no model that permits to predict the diffusion degree in a room from the values of absorption and diffusion coefficients of the walls in a room. So diffusion seems a problem more complicated that reverberation in the sense that reverberation can be predicted if one knows the absorption coefficients of the walls. In the present work we perform a review of some of the classical methods to evaluate the diffusion degree in a room. Some important mismatches between these methods are shown. CHARACTERIZATION OF THE DIFFUSORS First step in our work has been to evaluate the acoustic parameters that characterize the scattering due to a diffuser in an anechoic chamber. As a starting point for our work we use a Diffractal diffuser. This kind of diffusers consists on a repetition of the generating sequence at to scales. This fact enlarges the bandwidth of the scattered sound an also avoid particular reflection directions. We have chose free field methods, so, the diffuser has been mounted on a turntable at a distance of 4 5 meters to a loudspeaker inside an anechoic chamber. Finally an omnidirectional microphone has been placed in a goniometer. All of the reflection angles for all of the incidence angles have been measured form 90 to 90 degrees with steps of 5 degrees. The impulse response measurement was obtained with a Clio Card operating with a 14MLS sequence. Appropriate time windowing was used in order to separate direct and reflected sound. Thus, we have obtained the reflected to incident intensity ratio, i.e. I ir 10 LIreflected LIincident /10 (1) From that, one can obtain the diffusion coefficients commonly used in order to evaluate the scattering due to the diffuser [1]: Diffuse Energy Total Energy () uc Iir I ir N 1 Iir (3) uc evaluates the uniformity of the scattered sound while compares the acoustic energy reflected in a diffuse way (out from the specular zone defined by the Snell law) and the total reflected energy (i.e. diffuse+specular). The relationship between these two coefficients depends on the form of the scattering pattern and on the distance between microphones and the diffuser. It is usually a nonlinear one of the form: uc n (4) with n greater than one. In our experiment n. UC 1 0,75 0,5 0, f(hz flat panel diffuser FIGURE 1. Comparative plot of the uc for the diffuser and for a flat panel of the same width.

27 EXPERIMENTAL SET-UP After having evaluated the scattering coefficients of the diffuser we have performed an experiment in order to study the increase of the diffusion degree of the acoustic field inside a room. For this purpose we have measured some of the parameters related with the diffusion in a room with and without diffusers inside of it. 80 ms d fallings p 5 ms 1 p dt (7) where p i are the acoustic pressures measured at different points (7 cm between then). The last parameter is the decrease of coloration obtained from the standard deviation of the power spectra. d coloration 1 ( power spectra) (8) Absorbent material Loudspeakers d LEF, d Area and d coloration take a value of 1 in perfect diffuse fields while d fallings goes to 0 in that case. ESPERIMENTAL RESULTS Measurement positions 1 m Glazed wall Table 1 shows the results for one of the positions evaluated. 1 6 m Rear wall (metallic) Diffuser FIGURE. Evaluated room. The floor is made of wood and the ceiling is made of plaster. The particular room evaluated is a rectangular one with large unhomogeneitys in absorption coefficients on its walls. (See Fig. ) Two loudspeakers were placed at 5 meters of a metallic wall (covered with diffusers in the second part of the experiment), with a distance between then of meters. We measured the impulse response of the system with several microphones. From the impulse response we have obtained a list of parameters related with diffusion. For the sake of brevity we present here the results for only 4 of them: 0'33 LEF d LEF 1 0'33 (5) Table 1. Experimental results Parameter Without diffusers With diffusers d LEF d Area d fall normalized d coloration The results for d coloration and d fallings show a growth of the diffusion degree when the diffusers are present in the room while d LEF and d Area show a decrease of it. This apparent contradiction between these parameters can be interpreted as follows: the diffusers enforce the lateral reflections making the sound field less isotropic. However another effect may be expected. The diffuse reflections redistribute the sound in time making the fall from stationary more gradual. Nevertheless this fact does not justify the decrease of d Area. ACKNOWLEDGMENTS We gratefully acknowledge fruitful discussions with X. Meynial (University of Lemans). where LEF stands for Lateral Energy Fraction and it is calculated as the quotient between the sound pressure measured with a 8-patern-directional microphone and an omnidirectional one integrated from 5 to 80 ms. (Evaluated from 50Hz to 1000Hz) (0 33 is the expected value of LEF for a perfectly diffuse field). Another parameter evaluated is the d Area defined as the quotient between the area below the line of the backward integrated decay in the plot of sound level pressure vs time, and the area below a straight line. (Spring and Randall[]) REFERENCES [1]. A. Farina, M. Zanolin, E. Crema. Measurement of sound scattering properties of diffusing panels through the Wave Field Synthesis approach. 108th AES Convention, Paris. 18- February 000 [].N.F. Spring, K.E. Randall. The measurement of the sound diffusion index in rooms. BBC Research Department Report (1969) 16

28 Control of sound fields in reverberating rooms : Time reversal and inverse filter S. Yon, M. Tanter and M. Fink. Laboratoire Ondes et Acoustique, CNRS UMR 7587, ESPCI, 10 rue Vauquelin Paris, France. The ability of controlling sound in a given zone of a room can be assimilated to the capacity of focusing acoustical energy, both temporally and spatially. Focusing sound in rooms is a complicated problem, essentially because of the multiple reflections on obstacles and walls that may occur during propagation. In order to obtain a good focusing quality, the two well known ultrasound techniques of time reversal and inverse filter have been applied to this specific problem. Compared to classical focusing techniques such as delay law focusing, time reversal and inverse filtering appear to considerably improve quality of both temporal and spatial focusing. This phenomenon is due to the ability of these techniques to compensate for the different sound paths between the emitting antenna and the focal point. Those systems also prove to be robust towards small modifications in the medium, such as moving people. After a short introduction to those techniques, experimental results are presented. Time reversal and inverse filter are compared, showing the respective advantages of each technique; and future applications are discussed. INTRODUCTION Control of sound fields is an interesting domain of application for room acoustics, with many applications such as noise control, or creation of virtual 3- dimensionnal sound (auralization). Many techniques have been developed in order to achieve this sound field control, such as Wave Field Synthesis [1]; however, most of them are unable to compensate for the restitution room, leading to noise due reflections against walls. SOUND CONTROL TECHNIQUES Two techniques used in ultrasound to focus acoustical energy in complex media can be used to obtain a sound field control in a reverberating room. Both are based upon the acquisition of a Propagation operator h mj (t), between a set of J emitters (loudspeakers in our situation) and a set of M control points located in the zone where sound field has to be controlled. Thus, when a set of signals e j (t) are emitted by the loudspeakers, signals measured on the control points can be written: J f t) = Σ h ( t) e ( t) ( (1) m mj j t j= 1 Both techniques of time reversal [] and Inverse filtering [3] aim to obtain a set of signals to emit e j (t), for a given objective sound field f 0 m () t. To obtain the signal, it is necessary to invert eq (1). On the one hand, time reversal provides a simple way to achieve this inversion: when the propagation occurs without attenuation, and when spatial reciprocity is respected, h jm (-t) provide a good approximation of the inverse operator. 0 I (db) Singular value number Hz FIGURE 1: Singular values space for free space (left), and reverberating room (right).

29 On the other hand, it is possible to obtain a direct approximation of the inverse operator by inverting the matrix in Fourier domain H mj (ω) for each frequency. As for every inverse problem, for this operation to be done properly, one must separate the physically significant part of the operator from measurement noise. This separation is obtained by achieving a singular value decomposition (SVD) of the operator for each frequency. Indeed, this decomposition let appear singular values with different weights, as shown by fig. 1. Interesting results can be observed with such a representation: indeed, physically relevant singular values represent the number of available degrees of freedom in the reconstruction of the desired sound field. Fig 1 Shows that in the circumstances of the experiment, a reverberating room is a more interesting propagation medium than free space, because with an identical configuration, more complicated sound field can be created. The main problem is to recreate this sound field. EXPERIMENTAL RESULTS Both time reversal and inverse filtering provide a way to use reverberation in the room to our advantage, and thus creating the desired sound field with precision. In order to evaluate the performance of the two techniques, the objective sound field is chosen to be a focal spot of width 0 -6dB, in the spatial dimension, and a impulsion with a Hz frequency range in the time domain. Results obtained with this objective field are presented in figures and 3. From both spatial and temporal point of view, Inverse filtering appears to give better results than time reversal. Especially, as shown in figure 3, temporal recompression is a lot more efficient for inverse filtering. 0-5 I (db) RT The main improvement coming from the use of inverse filtering is indeed the fact that the spectrum variations are compensated during the process. Thus, temporal responses are optimized both in their width and their level of sidelobe level. However, figure show that improvement in terms of spatials focusing are not very strong, especially when the overall energetic efficiency is considered: SPL level obtained at focal point with time reversal is 10 db above level obtained with inverse filtering t (ms) Inverse filtering Time reversal FIGURE 3: Quality of temporal compression for the two techniques. CONCLUSION Reverberant rooms are very interesting media to obtain a shaping of the sound field. Use of reverberations is however tricky, and imply the use of powerful sound shaping techniques. Of the two described techniques, inverse filter is more efficient for audio applications, because of its ability to compensate spectrum variations. However, time reversal is easier to implement in practical systems, especially when not a lot of computing power is available IF, M=1 REFERENCES IF, M= IF, M=5 distance to focal point (cm) Berkhaut, De Vrie and Vogel, Acoustic control by wave field synthesis, J. Acous. Soc. Am. 93(5), pp (1993). M. Fink, Time reversed acoustics, Physics Today, pp , march Tanter, Aubry, Gerber, Thomas & Fink, optimal focusing by spatio-temporal inverse filter part I.: Basic principles, J. Acous. Soc. Am, Accepted for publication. FIGURE : Focusing obtained with the two techniques for a spatial impulse response.