Ray-tracing prediction of optimal conditions for speech in realistic classrooms

Recent papers have discussed the optimal reverberation times in classrooms for speech intelligibility, based on the assumption of a diffuse sound field. Here this question was investigated for more ‘typical’ classrooms with non-diffuse sound fields. A ray-tracing model was modified to predict speech-intelligibility metric U₅₀. It was used to predict U₅₀ in various classroom configurations for various values of the room absorption, allowing the optimal absorption (that predicting the highest U₅₀)—and the corresponding optimal reverberation time—to be identified in each case. The range of absorptions and reverberation times corresponding to high speech intelligibility were also predicted in each case. Optimal reverberation times were also predicted from the optimal surface-absorption coefficients using Sabine and Eyring versions of diffuse-field theory, and using the diffuse-field expression of Hodgson and Nosal. In order to validate the ray-tracing model, predictions were made for three classrooms with highly diffuse sound fields; these were compared to values obtained by the diffuse-field models, with good agreement. The methods were then applied to three ‘typical’ classrooms with non-diffuse fields. Optimal reverberation times increased with room volume and noise level to over 1 s. The accuracy of the Hodgson and Nosal expression varied with classroom size and noise level. The optimal average surface-absorption coefficients varied from 0.19 to 0.83 in the different classroom configurations tested. High speech intelligibility was, in general, predicted for a wide range of coefficients, but could not be obtained in a large, noisy classroom.     

Statistical comparison of reverberation times measured by the integrated impulse response and interrupted noise methods, computationally simulated with ODEON software, and calculated by Sabine, Eyring and Arau-Puchades’ formulas

This paper evaluates several procedures to determine the reverberation time, RT, in a classroom. These procedures are: (1) measurement by the integrated impulse response method, (2) measurement by the interrupted noise method, (3) computer simulation using ODEON Version 9.0 software, and (4) calculations using the Sabine, Eyring, and Arau-Puchades formulas. The resulting data are analyzed statistically to verify their similarity. No statistical difference was found between the values obtained by the two measuring methods. The computer simulation produced accurate data. The best formula for calculating RT in the classroom in question is Eyring’s formula.     

On site validation of sound absorption measurements of occupied pews

Laboratory measurements of sound absorption by audiences are known to be scarcely reliable when applied to actual rooms as a consequence of several problems, among which the different area of the “sample” and the different distribution of the reflected sound may play important roles. When dealing with worship places, characterized by a variable degree of occupation and much lower absorption due to unoccupied seats, things become more complicated as absorption seems to be proportional to the number of occupants rather than to the area they cover (as normally accepted in performing spaces). The combination of these variables has been investigated by taking advantage of laboratory measurements and analysing their application to six churches, where on site measurements of reverberation time were carried out with and without occupation. The results are discussed both in terms of simple prediction formulae (Sabine, Eyring, and Arau-Purchades) and of computer simulations, showing that laboratory measurements may be reliably used in computer simulations (at least in the frequency range from 500 Hz on). At low frequencies greater attention must be paid as the absorption coefficients need to be corrected as a function of the actual distribution of the sound field in the room.     

Comparison between measured and calculated parameters for the acoustical characterization of small classrooms

This paper presents a comparison between measured and calculated acoustical parameters in eight high school classrooms. The mid frequency unoccupied and occupied reverberation times and the 1 kHz sound propagation (SP) of the reverberant and total speech levels in occupied classrooms were compared with analytical and numerical predictions. The ODEON 6.5 code and the Sabine formula gave the most accurate results for reverberation time in the empty classrooms with overall relative differences of 8.1% and 9.7%, respectively. With students present, the Eyring and Sabine formulas and Hodgson’s empirical model resulted to be the most accurate with relative differences of 11.1%, 13.2% and 13.6%, respectively. The reverberant speech levels decrease with increasing distance from the source at rates varying from −1.21 to −2.62 dB/distance doubling, and the Hodgson model fits the slope values quite well. The best predictions of the SP of the reverberant and total speech levels are shown, in order of accuracy, for the ODEON code, the Barron and Lee theory and the classical diffuse field theory. Lower rms errors were found when the measured total acoustic absorptions were used. The lowest rms error of 1.4 dB for the SP of the total speech level were found for both the ODEON code and the Barron and Lee theory.     

Predicting reverberation times in a simulated classroom

By varying the sound-absorption treatments in a simulated classroom, experimental results were compared with analytical and computer predictions of reverberation time. Analytical predictions were made with different absorption exponents, which are the result of different weighting procedures involving room surface areas and the sound-absorption coefficients. Sound scattering was found to influence measured reverberation times. With the amount of sound scattering provided, more accurate analytical predictions were obtained with absorption exponents that give reverberation times longer than those obtained with the Sabine absorption exponent, which consistently underpredicted reverberation times. However, none of the absorption exponents could be singled out as more adequate because of similar average accuracy. Computer predictions of reverberation time were accomplished with two commercially available ray-based programs, RAYNOISE 3.0 and ODEON 2.6, with specular and calibrated diffuse reflection procedures. Neither type of procedure, in either program, was more accurate than the best analytical predictions. With RAYNOISE, neither the specular nor the calibrated diffuse reflection procedure could be singled out as more adequate. For ODEON, the calibrated diffuse reflection procedure gave consistently more accurate predictions than its specular reflection procedure, with the best accuracy of the computer predictions.     

Laboratory measurement of sound absorption of occupied pews and standing audiences

Places of worship, as well as other performing spaces or large arenas are characterized by lightweight pews or seats, with moderate or negligible upholstery, leading to very low absorption coefficients. Consequently, the audience becomes the most important sound absorbing element, capable of playing a fundamental role in determining the acoustic characteristics of the space. Consequently accurate knowledge of its acoustic properties is required for any design purpose. Several studies have been carried out with reference to audiences seated on upholstered theatre seats but there is a considerable lack of information about occupied pews. The well known difficulty of taking into account edge effects during such measurements poses further questions as well as the effect of the density of occupation, and the seasonal variations due to clothing. This paper presents the results of a series of laboratory measurements aimed at clarifying such aspects. The measurements showed that the edge effects are negligible and that total absorption is better related to the number of persons present than to the area they cover. Nonetheless, as the density grows, or when the audience is seated, there is a reduction in absorption which may be explained by the reduction in exposed body surface. Lightweight clothes show a considerable reduction in sound absorption over all the frequency bands, suggesting that significant seasonal fluctuations in reverberation time should be expected in places where the audience is the only sound absorbing surface.     

Applicability of locally reacting boundary conditions to porous material layer backed by rigid wall: Wave-based numerical study in non-diffuse sound field with unevenly distributed sound absorbing surfaces

To clarify the applicability of locally reacting boundary conditions in wave-based numerical analyses of sound fields in rooms, we numerically analyzed a non-diffuse sound field in a room with unevenly distributed sound absorbing surfaces and investigated the differences between the extended and local reactions. Each absorbing surface was a porous material layer backed by a rigid wall. Simulations were performed by the fast multipole boundary element method, a highly efficient boundary element method using the fast multipole method. At low frequencies, the extended and local reactions yielded similar reverberation decay curves because of the influence of the room. However, when the random incidence absorption coefficients were small at low frequencies or frequencies were high, the difference was greater than expected from the corresponding Eyring decay lines. We conclude at high frequencies, the locally reacting boundary conditions lead to a longer reverberation time than that expected from the absorption coefficient differences between the extended and local reactions. These differences were similar in sound-pressure-level and sound-intensity-level distributions, and in the oblique incidence absorption coefficient of the absorbing surfaces, but were increased at low frequencies.     

Effects of edge screens on the absorption of blocks of theatre chairs

This paper reports new measurement results investigating the use of screens around samples of theatre chairs to minimize edge effects when measuring theatre chair absorption in reverberation chambers. The absorption measurements included both full scale and scale model measurements in reverberation chambers and a model recital hall. The use of screens has been proposed to better approximate the sound absorption of the larger blocks of chairs in auditoria. The method of measuring the absorption of blocks of chairs with screens around their edges and located in the corner of a reverberation chamber did not give results indicative of the values obtained for larger areas in auditoria. The addition of screens around samples of chairs did not eliminate the variation of absorption coefficients with perimeter/area ratio. The results of extrapolations from measurements of blocks of screened chairs to infinite samples gave lower absorption coefficients than found for blocks of unscreened chairs. The absorption of chairs in large performance halls can best be predicted using the P/A method to extrapolate from reverberation chamber measurements of smaller samples of unscreened chairs, with a range of P/A values, to the larger samples and lower P/A ratios of blocks of chairs typical of performance spaces.     

An investigation of the sound field above the audience in large lecture halls with a scale model

Measurements of steady-state sound pressure levels above the audience in large lecture halls show that the classical equation for predicting the sound pressure level is not accurate. The direct field above the seats was measured on a 1:10 scale model and was found to be dependent on the incidence angle and direction of sound propagation across the audience. The reverberant field above the seats in the model was calculated by subtracting the direct field from the measured total field and was found to be dependent on the magnitude and particularly on the placement of absorption. The decrease of sound pressure level versus distance in the total field depends on the angle (controlled by absorption placement) at which the strong reflections are incident upon the audience area. Sound pressure level decreases at a fairly constant rate with distance from the sound source in both the direct and reverberant field, and the decrease rate depends strongly on the absorption placement. The lowest rate of decay occurs when the side walls are absorptive, and both the ceiling and rear wall are reflective. These consequences are discussed with respect to prediction of speech intelligibility.     

Influence of absorption properties of materials on the accuracy of simulated acoustical measures in 1:10 scale model test

This study investigated the absorption characteristics of materials in a multi-purpose hall using computer models, 1:10 scale model and actual hall measurements of Gimhae Arts Hall (GAH), in order to predict and evaluate the acoustical characteristics. The elements of this scale model, such as reflecting walls, seats, audience, and absorption banners, were made with materials selected according to their absorption coefficients, measured in a 1:10 scale model reverberation chamber. After the real hall was completed, in situ acoustical measurements were conducted in the GAH and compared with those of the scale model hall. Comparison of these measurements showed that the delay time of the major reflections in the scale model hall was similar to that of the real hall. However, the reverberation time especially at low frequencies showed a difference between the scale model hall and the real hall measurements. The results of computer simulations for both scale model and actual hall showed that the absorption of seats and audience, the structural detail of the reflecting walls with different thickness and air spaces, and the duct facilities in the open-type ceiling are the major differences. It was confirmed that there are more complicated absorption characteristics in the scale model design of a multi-purpose hall than a concert hall.     

Sound strength and reverberation time in small concert halls

Sound strength and reverberation time measurements have been carried out in six small concert halls in Cambridge, UK. The sound strength G is a measure of the physical sound level in a concert hall and is closely related to the subjective sensation of loudness. It compares integrated impulse responses at a point in the measured room with that measured at ten metres distance in the free field.The aim of the measurements is to investigate the acoustic characteristics of the halls concerning sound strength and reverberation time. Furthermore the effect of the variable acoustics in the halls on these parameters is discussed in this paper. Especially for bigger ensembles it is often desirable to reduce the sound level in a small concert hall. The measurement results show that for a fixed hall volume, this can primarily be achieved by decreasing the reverberation time in the hall. However, with regard to the sound quality of a hall and the recommended reverberation times for chamber music, reverberation time cannot be reduced by an arbitrary extent. Therefore reverberation time and strength have to be balanced very carefully in order to obtain sufficient reverberation whilst at the same time avoiding excessive loudness. Finally the measured strength levels are compared to values derived from traditional and revised theory [Barron M, Lee L-J. Energy relations in concert auditoriums. J Acoust Soc Am 1988;84(2):618-28] on strength calculations in order to assess the accuracy of the theory for small chamber music halls. Possible reasons for the low measured strength levels observed are discussed with reference to related design features and objective acoustic parameters.     

Über den optimalen nachhall in kleinen bis mittelgrossen kirchen

The reverberation times of churches should be longer, for example, than those of theatres or concert halls but they must not be too long. By means of an examination of small and medium sized churches, a relation between measured reverberation times and judgments of acoustical qualities is established in this paper. From this relation, an optimum range of average reverberation times, $\text{T}{}_{\mathrm{m}}$, of unoccupied churches at 500 Hz and 1000 Hz octave bands can be derived as a function of volumes extending from 1000 m³ to 12 000 m³.     

A modified diffusion equation for room-acoustic predication

This letter presents a modified diffusion model using an Eyring absorption coefficient to predict the reverberation time and sound pressure distributions in enclosures. While the original diffusion model [Ollendorff, Acustica 21, 236-245 (1969); J. Picaut et al., Acustica 83, 614-621 (1997); Valeau et al., J. Acoust. Soc. Am. 119, 1504-1513 (2006)] usually has good performance for low absorption, the modified diffusion model yields more satisfactory results for both low and high absorption. Comparisons among the modified model, the original model, a geometrical-acoustics model, and several well-established theories in terms of reverberation times and sound pressure level distributions, indicate significantly improved prediction accuracy by the modification.     

A possible acoustic design approach for multi-purpose auditoria suitable for both speech and music

In several auditoria, it has been observed that the reverberation time is longer than expected and that the cause is a horizontal reverberant field established in the region near the ceiling, a field which is remote from the sound absorbing audience. This has been observed in the Boston Symphony Hall, Massachusetts, and the Stadthalle Göttingen, Germany. Subjective remarks on their acoustics suggest that there are no unfavourable comments linked to the secondary sound field. Two acoustic scale models are considered here. In a generic rectangular concert hall model, the walls and ceiling contained openings in which either plane or scattering panels could be placed. With plane panels, the model reverberation time (RT) was measured as 53% higher than the Sabine prediction (frequency 500/1000 Hz), compared with 8% higher with scattering panels. The second model of a 300 seat lecture theatre with a 6 m or 8 m high ceiling had raked seating. In this case, the amount of absorption in the model was increased until the point was reached where speech had acceptable intelligibility, with the early energy fraction, D ? 0.5. For this acceptable speech condition with the 6 m ceiling, the measured mid-frequency T₁₅ was 1.47 s, whereas the Sabine predicted RT was 1.06 s. The sound decay was basically non-linear with T₃₀ > T₁₅ > EDT. Exploiting a high-level horizontal reverberant field offers the possibility of acoustics that are better adapted as suitable for both speech and unamplified music, without any physical change in the auditorium. Using secondary reverberation in an auditorium for a wide variety of music might also be beneficial.     

Some acoustical properties of St Paul's Cathedral,London

The interior of St Paul's Cathedral has a volume of 152 000 m³ including the large dome. The average value of the reverberation time is 11 s at 500 Hz when the cathedral is empty and reduces to 7·8 s at the same frequency when the cathedral is full. These measurements have been confirmed by several methods, including the method of integrated impulses. For frequencies above 1250 Hz the reverberation time decreases, because of air absorption and the special effect of the dome. With a steady random noise source the energy density was not constant in the nave: at 1000 Hz the sound level fell away at an approximate rate of 3 dB per doubling of distance. The assumption of a Sabine space can be made to some extent, and based on this assumption it is possible to estimate the reverberation time when the cathedral is full from the results when empty. Speech intelligibility is poor and articulation tests showed that in the middle of the nave only 20–30% of words are understood.     

Prediction of energy decay in room impulse responses simulated with an image-source model

A method is proposed that provides an approximation of the acoustic energy decay (energy-time curve) in room impulse responses generated using the image-source technique. A geometrical analysis of the image-source principle leads to a closed-form expression describing the energy decay curve, with the resulting formula being valid for a uniform as well as nonuniform definition of the enclosure's six absorption coefficients. The accuracy of the proposed approximation is demonstrated on the basis of impulse-response simulations involving various room sizes and reverberation levels, with uniform and nonuniform sound absorption coefficients. An application example for the proposed method is illustrated by considering the task of predicting an enclosure's reflection coefficients in order to achieve a specific reverberation level. The technique presented in this work enables designers to undertake a preliminary analysis of a simulated reverberant environment without the need for time-consuming image-method simulations.     

On boundary conditions for the diffusion equation in room-acoustic prediction: Theory, simulations, and experiments

This paper proposes a modified boundary condition to improve the room-acoustic prediction accuracy of a diffusion equation model. Previous boundary conditions for the diffusion equation model have certain limitations which restrict its application to a certain number of room types. The boundary condition employing the Sabine absorption coefficient [V. Valeau et al., J. Acoust. Soc. Am. 119, 1504-1513 (2006)] cannot predict the sound field well when the absorption coefficient is high, while the boundary condition employing the Eyring absorption coefficient [Y. Jing and N. Xiang, J. Acoust. Soc. Am. 121, 3284-3287 (2007); A. Billon et al., Appl. Acoust. 69, (2008)] has a singularity whenever any surface material has an absorption coefficient of 1.0. The modified boundary condition is derived based on an analogy between sound propagation and light propagation. Simulated and experimental data are compared to verify the modified boundary condition in terms of room-acoustic parameter prediction. The results of this comparison suggest that the modified boundary condition is valid for a range of absorption coefficient values and successfully eliminates the singularity problem.     

Investigating the absorption characteristics of open ceilings in multi-purpose halls using a 1:25 scale model

This paper investigated the absorption coefficients of acoustically transparent ceilings using 1:25 scale models. From a field survey of 18 existing halls, it was found that the open ceilings were equipped with steel truss structures, ducts, catwalks and ceiling surfaces. In order to investigate the absorption characteristics of the equipped ceilings, measurements were made using a 1:25 reverberation chamber based on ISO 354. Results showed that for an empty ceiling with a depth of 6 m, the absorption coefficient with a 50%-perforated ceiling surface is 0.2-0.3 above 500 Hz. If there were steel structures inside the ceiling, the absorption coefficient increased by 0.1 at 125 Hz to 2 kHz. Adding ducts and catwalks increased the absorption by 1-2 kHz. The absorption coefficients of the equipped ceilings ranged from 0.19 to 0.61 and the absorption characteristics were mainly found at high frequencies. Maximum absorption was observed in heavily equipped ceiling structures.     

Acoustic characterization of on-stage performers in performing spaces

The influence of on-stage performers on the acoustic characteristics of performing spaces is significant because the musicians are absorptive and close to the sound source. However, the acoustic information of the musicians and their effect on absorption, scattering, and diffusion remain unclear. The acoustic characteristics of musicians were measured in a reverberation chamber and a semi-anechoic chamber while varying the type of clothes, the instruments, and seating density. The clothing worn showed a larger impact on the absorption per person, whereas the addition of cellos resulted in low-frequency absorption per person. The addition of cellos also increased the scattering and diffusion characteristics. Finally, the total absorption by the musicians under various conditions was analyzed in a concert hall using the simple Sabine equation where the influence of the musician’s instruments resulted in reverberation time of more than 0.1 s decrease with about 90 musicians on stage. However, the influences of additional musical instruments resulted in no significant difference in the reverberation time compared to the people alone. In addition, scattering due to the various conditions of orchestra such as the seating density and the addition of musical instrument was not a significant predictor of reverberation time.     

Prediction of the reverberation time in high absorbent room using a modified-diffusion model

A modification of the diffusion model’s boundary condition, based on the Eyring absorption coefficient, to account for high walls absorption is proposed. Numerical comparisons are carried out for three geometrical configurations (a proportionate room, a corridor and a flat enclosure). Comparisons with the statistical theory and a ray-tracing software show that the modified boundary condition increases the accuracy of the diffusion model in term of reverberation time in all the simulated configurations. An experimental comparison in the case of a non-uniformly absorbent room (a reverberation chamber covered with patches of glass wool) is also carried out. The modified-diffusion model results match well with the ray-tracing ones. Both models are in agreement with the experimental data for most of third octave bands (discrepancy close to or below 10%). However, some discrepancies up to 40% can also be observed in a few octave bands, probably due to experimental considerations and to the modal behaviour of the room at low frequencies.