A WRITE-UP ON

SIMULATED CONCERT HALL ACOUSTICS

COMPILED BY

BANJO-OGUNLEYE TELEMI ARC/09/7370

KASSIM O.A. ARC/09/7391

COURSE

ARC 507

ENVIRONMENTAL CONTROL III

(ACOUSTICS AND NOISE CONTROL)

COURSE LECTURER

PROF. OLU OLA OGUNSOTE

SUBMITTED TO

THE DEPARTMENT OF ARCHITECTURE

SCHOOL OF ENVIRONMENTAL TECHNOLOGY

FEDERAL UNIVERSITY OF TECHNOOLOGY, AKURE

JULY, 20141

1.0 SUMMARY

A concert hall is a cultural building which serves as a performance venue, chiefly for classical instrumental music. Many concert halls exist as one of several halls or performance spaces within a larger performing arts center and, where appropriate, the name of the arts centre is included. Decibel levels, decay time, attenuation over time and so on are the major factors upon which the acoustic properties of a standard and effective concert hall depend. Acoustic simulation of spaces has been used in recent times to achieve the desired acoustic environment and thus averts the cost of re-engineering after construction in the event of acoustic failure.

This paper therefore talks about the methods in which Acoustic simulation coul be achieved effectively and accurately, they include; image source methods, radiant exchange methods, statistical methods, ray-tracing and beam as result oriented approaches used with varying history of success. However, a variety of hybrid techniques such as the Inverse Optimization technique has been effectively used for the simulation of concert halls.

2.0 INTRODUCTION

The way sound waves react on contact with various materials, shapes and structures, is of fundamental interest in acoustics. It is of concern in architectural design, customization of auditorium and room acoustics, and in design of convincing auralizations of acoustical situations for virtual reality applications. The materials, shapes and structures determine the way sound energy is absorbed, reflected or transmitted, and the extent and quality of the spatial and temporal dispersion inherent in the reflections. These factors then contribute to a range of perceptually important acoustic properties such as the reverberation time of the space, the diffuseness of the sound field, and generally the way a sound source is translated through the acoustic space to a listener.

A concert hall is a public building which is mainly designed for the purpose of performing music and for holding concerts. In the early times, around 18th century, some concert halls were built which were favored and said to be masterpiece, example of which are Vienna’s Grosser Misikvereinssall (built 1870), Leipzig’s Gewandhaus (1885) and symphony hall in Boston (1900), a time when engineering and architectural techniques were still in their infancy compared with the last half of the twentieth century. Due to the limiting span of roofs and other technological limitations that posed at these periods, most of these ancient adorable European halls achieved their superior acoustic quality by accident, the reason being that they had to be built narrow and in a strict rectilinear form.

Acoustic efficiency is however a desire that varies essentially with the intended use of a space besides its enhancement been related to a number of subjective factors combining to make the whole process a complex task. Acoustic design is thus difficult because the human perception of sound depends on such things as decibel level, direction of propagation, and attenuation over time—none of which are tangible or visible.

In a bid to achieve acoustics in time past, designers build physical scale model and tested them visually and acoustically by coating the interiors of the models with reflective material and then shining lasers

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from various source positions, they assess the sight and sound lines of the audience in a hall. These approach seem to be accurate because of the its level of meticulousness, but then these traditional methods have proven inflexible, costly and time- consuming to implement, they have also created some major acoustic failures. The advent of computer simulation and visualization techniques for acoustic design and analysis has yielded a variety of approaches for modelling acoustic performance. These techniques have been addressing the accuracy and speed of simulation, offering effective visualization or auralization of the resulting multi-dimensional data of simulation.

However, while these techniques certainly offer new insights into acoustic design, they fail to enhance the design process itself, which still involves a burdensome iterative process of trial and error. For instance, financial concerns might dictate a larger hall with increased seating capacity. This can have negative effects on the hall’s acoustics, such as excessive reverberation and noticeable gaps between direct and reverberant sound. Fan-shaped halls bring the audience closer to the stage than other configurations, but they may fail to make the listener feel surrounded by the sound. The application of highly absorbent materials may reduce disturbing echoes, but they may also deaden the hall. A concert hall’s acoustics depends on the designer’s ability to balance many factors.

After a wide range of research has been carried out, Acoustic Simulation has been divided into five general categories which are;

1. Image source methods2. Statistical methods3. Ray tracing methods4. Radiant exchange methods5. Beam tracing methods

A variety of hybrid simulation techniques also exist which typically approximate the sound field by modelling the early and late sound fields separately and combining the results. One of such hybrid systems is the Inverse Optimization simulation engine. In this write-up, the highlights of the simulation system shall be discussed especially that of the concert halls.

3.0 ARCHITECTURAL ACOUSTICS HISTORY

It is quite expedient to know the background of architectural acoustics before moving into details of the simulated concert hall acoustics.

Once a decent hall was designed, architects would copy the model in an attempt to achieve the same acoustics, but no one understood well what made one hall sound wonderful and another appalling. As a result, many concert halls failed and were destroyed in the process of natural selection. In the past century, however, the study of architectural acoustics has developed into a more precise science.

Architectural acoustics (also known as room acoustics and building acoustics) is the science and engineering of achieving a good sound within a building and is a branch of acoustical engineering. The first application of modern scientific methods to architectural acoustics was carried out by Wallace Sabine in the Fogg Museum lecture room who then applied his new found knowledge to the design of Symphony Hall, Boston. Architectural acoustics can be about achieving good speech intelligibility in a

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theatre, restaurant or railway station, enhancing the quality of music in a concert hall or recording studio, or suppressing noise to make offices and homes more productive and pleasant places to work and live in. Architectural acoustic design is usually done by acoustic consultants.

The beginnings of architectural acoustics as a science originated at Harvard University's Fogg Art Museum. Soon after the museum was built in 1895, it was determined that its lecture hall had absolutely atrocious acoustics. Wallace Clement Sabine, a young physics professor, was asked to help. For the next three years, Sabine delved into the task of scientifically testing the room acoustics, using a stopwatch, organ pipes and a number of seat cushions. Fogg Art Museum's lecture hall never did measure up to standards for acceptable speech intelligibility and was eventually torn down. However, while attempting to fix the acoustics, Sabine developed a foundation for the science of architectural acoustics. He formulated an equation for reverberation time, relating it to room volume and materials. The unit for a material's sound absorption, the sabin, is named after him.Wallace Sabine is thus viewed as the father of modern architectural acoustics. He was the first to quantify and measure factors that contribute to suitable room acoustics. Since Sabine's experiments, physicists and engineers have found that good acoustics depends on much more than just reverberation time. These parameters, as well as the concept of reverberation time, are explained further in the Discussion section.

4.0 SIMULATED ACOUSTIC METHODS

Three of the five general techniques of acoustic simulation will be considered here;

4.1 RAY-TRACING METHOD

The Ray Tracing Method uses a large number of perticles, which are emitted in various directions from a source point. The particles are traced around the room loosing energy at each reflection according to the absorption coefficient of the surface. When a particle hits a surface it is reflected, which means that a new direction of propagation is determined according to snell’s law as known from geometrical optics. This is called a specular reflection. In order to obtain a calculation result related to a specific receiver position, it is necessary either to define an area or a volume around the receiver in order to catch the particles when travelling by, or the sound rays may be considered the axis of a wedge or pyramid. In any case there is a risk of collecting false reflections and that some possible reflection paths are not found. There is a reasonably high probaility that a ray will discover a surface with the area A after having travelled the time t if the area of the wave front per ray is not larger than A/2. This leads to the minimum number of rays N

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Where c is the speed of sound in air. According to this equation a very large number of rays is necessary for a typical room. As an example a surface area of 10m² and a propagation time up to only 600ms lead to around 100,000 rays as a minimum.

The development of the room acoustical ray tracing models started some thirty year ago but the first models were mainly meant to give plots for visual inspection of the distribution of reflections. The method was further developed and in order to calculate a point response the rays were transferred into circular cones with special density functions, which should compensate for the overlap between neighboring cones. However, it was not possible to obtain a reasonable accuracy with this technique. Recently, ray tracing models have been developed that use triangular pyramids instead of circular cones, and this may be a way to overcome the problem of overlapping cones.

The Figure 1.0 presents a model of a concert hall with direct sound and all the first- and second-order reflection paths obtained by ray-tracing. The geometrical model of the hall contains ca. 300 polygons and 40,000 rays were emitted uniformly over a sphere. The model represents the Sigyn concert hall in Turku, Finland.

Figure 1: The direct sound and first- and second-order reflection paths in a concert hall obtained by a ray-tracing simulation. The source and the listener are denoted by and , respectively.

4.2 THE IMAGE SOURCE METHOD

The Image Source Method is based on the principle that a specula reflection can be constructed geometrically by mirroring the source in the plane of the reflecting surface. In a rectangular box shaped room it is very simple to construct all image sources up to a certain order of reflection, and from this it can be deduced that if the volume of the room is V, the approximate number of image sources withn a

radius of ct is

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This is an estimate of the number of reflections that will arrive at a receiver up to the time t after sound emission, and statistically this equation holds for any room geometry. In a typical auditorium there is often a higher density of early reflections, but this will be compensated by fewer late reflections, so on average the number of reflections increases with time in the third power according to the immediate above equation.

The advantage of the image source methods is that it is very accurate, but if the room is not a simple rectangular box there is a problem. With n surfaces there will be n possible image sources of first order and each of these can create (n-1) second order image sources. Up to the reflection order i the number of possible image sources N will be

N= 1 + n/(n-2)((n-1)ͥ -1) ≈ (n-1)ͥ .

As an example, we consider a 1,500m³ room modelled by 30 surfaces. The mean free path will be around 16m which means that in order to calculate reflections up to 600ms a reflection order of i=13 is needed. Thus equation 3 shows that the number of possible image sources is approximately N=29^13≈10^19. The calculations explode because of the exponential increase with reflection order. If a specific receiver position is considered it turns out that most of the image sources do not contribute refections, so most of the calculation efforts will be in vain. From equation 2 it appears that less than 2500 of the 10^19 image sources are valid for a specific receiver. For this reason image source models are only used for simple rectangular rooms or in such cases where low order reflections are sufficient, e.g for design of loud speaker systems in non-reverberant enclosures.

Figure 2.0: In the image-source method the sound source is reflected at each surface to produce image

sources which represent the corresponding reflection paths. The image sources and representing first- and second-order reflections from the ceiling are visible to the listener while the reflection from

the floor is obscured by the balcony [P3].

Figure 2: The image-source method showing the sound source being reflected at each surface...

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4.3 STATISTICAL METHOD

In statistical acoustics, no attention is being paid to particular sound reflections. Instead of tracing the way of sound energy, statistically important characteristics of particular parts of the scene are collected to form the basis for computations. Statistical approach can be used for establishing values of reverberation time.

5.0 THE INVERSE OPTIMIZATION ACOUSTIC SIMULATION SYSTEM

The inverse interactive acoustic design approach is an effective simulation system that helps the designer produce an architectural configuration that achieves a desired acoustic performance. The system allows users to constrain changes to the environment and specify acoustic performance goals as a function of time. For new halls the system may suggest optimal geometric configuration that would not otherwise be considered, while for halls with modifiable components or renovation projects it may assist in optimizing the existing configuration. The advent of computer simulation and visualization techniques for acoustic design and analysis has yielded a variety of approaches for modelling acoustic performance. Most acoustic simulation packages have effectively addressed the accuracy and speed of the simulation algorithms and offered effective visualizations or auralizations of the resulting multidimensional data.

Generally, most of the acoustic simulation techniques are based on the direct method: those that compute a solution from a complete description of an environment and relevant parameters. Such systems can be very useful in the evaluating the performance of a 3D environment. This is however tedious as users are responsible for specifying input parameters and for evaluating the result, while the computer is only responsible for computing and displaying the results of these simulations. However, the Optimization simulation technique provides an alternative approach to design. This is the inverse method in which users are allowed to create a target and have the algorithm work backward to establish various parameters. The Optimization method employs a hybrid simulation engine, which models using the good qualities of the beam tracing and statistical acoustic simulation technique at various stages of modelling.

The simulation engine has several characteristic relevant to works on the acoustics of concert halls. Firstly, the geometric pre-processing step of the engine is independent of location and time; the designer can therefore specify a receiver’s location at any stage of design and obtain a set of acoustic data merely by sampling the precalculated sound field.

Secondly, the system has enormous potentials particularly in specifying appropriate surfacing materials in halls. This is however of great importance since the cost of modifying surfacing material is a small fraction of the cost of modifying its geometry (Changes in geometry invalidate a portion of the beam tree data structure and therefore requires its reconstruction, while changes in materials require only that the energy contributions of affected beams be updated.

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The system also;

1. Allow the designer to constrain changes to the environment and specify acoustic performance goals.

2. The system constrains the design process by specifying a range of allowable materials.3. It allows the designer to specify goals for acoustic performance in space and time through high-

level acoustic qualities such as decay time and sound level.4. It visualization tool facilitates an intuitive assessment of the complex time dependent nature of

sound, providing means of expressing desired performance

5.1 CHARACTERIZATION OF SOUND UNDER THE INVERSE OPTIMIZATION SYSTEM.

The Inverse optimization system adopts six statistically independent objective acoustic measures in characterizing the subjective impression of human listeners. These evaluation approach known as the Objective Rating Method (ORM) is accompanied by a visualization technique used to evaluate them. These six statistically orthogonal acoustic measures form the basis of the analysis and optimization work. While two of the measures, SDI (Surface diffusivity index) and TI, are single values representing the entire hall, the others are computed by averaging the values sampled at multiple spatial positions.

5.1.1 INTERAURAL CROSS-CORRELATION COEFFICIENT.

IACC is a biural measure of the correlation between the signals at the two ears of a listener. It characterizes how surrounded a listener feels by the sound within a hall. If the sound comes from directly in front of or behind the listener, it will arrive at both ears at the same time with complete correlation, producing no stereo effect. If it comes from another direction, the two signals will be out of phase and less correlated, giving the listener the desirable sensation of being enveloped by the sound. The correlation values depend on the arrival direction of the wave with respect to the listener’s orientation. The inverse optimization system uses cylinder to represent a receiver in a performance space. The graphical icon we use to represent IACC is a shell located on the sides of each listener icon. The greater the degree of encirclement of the icon by the shell, the more desirable is the IACC value.

5.1.2 EARLY DECAY TIME

EDT measures the reverberation or liveliness of a hall. Musicians characterize a hall as “dead” or “live,” depending on whether EDT is too low or high. The formal definition of EDT is the time it takes for the level of sound to drop 10 decibels from its initial level, which is then normalized for comparison to traditional measures of reverberation. The best values of EDT range between 2.0 and 2.3 seconds for concert halls.

The inverse optimization system uses a cone icon in which the height is fixed and the radius is scaled according to the decay time. For a value of 2.0 seconds, the cone is twice the width of the listener icon.

5.1.3 BASS RATIO

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BR measures how much sound comes from bass, reflecting the persistence of low-frequency energy relative to mid-frequency energy. Musicians refer to BR as the “warmth” of the sound. BR is defined as

BR - 125 + RT250

RT 500 + RT1000

The graphical icon used to represent BR at a receiver position consists of a pair of stacked, concentric cylinders of slightly different widths .The top cylinder represents the mid-frequency energy, from the 500-Hz and 1,000-Hz bands, and the bottom cylinder represents the lower frequency energy, from the 125-Hz and 250-Hz bands. The height of each cylinder represents the relative values in the ratio, assuming a constant combined height. A listener icon representing a desirable BR value of 1.25 would have the top of the lower cylinder just above the halfway mark. BR varies spatially throughout a hall.

5.1.4 STRENGTH FACTOR (G)

This factor measures sound level, approximating a general perception of loudness of the sound in a space. For a given location within the hall, G is the ratio of the sound energy arriving at that location from a non directional source to the direct sound energy measured at a distance of 10 meters from the

same source.

By using this ratio, the influence of source power is removed from the loudness calculation, allowing easy comparison of measured data across different halls.

The preferred values for G range between 4.0 dB and 5.5 dB for concert halls. In general, G is higher at locations closer to the source. It is instructive to see how the sound level changes through time, as well as location. We perceive a reflected wave front as an echo—perceptibly separable from the initial sound—if it arrives more than 50 ms after the direct sound and if it is substantially stronger than its neighbours. The time distribution of sound also affects our perception of clarity. Two locations in a hall may have the same value of G, but if the energy arrives later with respect to the direct sound for one location than the other, speech will be less intelligible and music less crisp. The Optimization system

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Figure 3: Glyphs representing IACC, EDT and BR

Source: Audi optimization Goal-Based Acoustic Design (2000)

uses colour to indicate relative scalar values of the sound-level data. It examines the accumulated sound-level data as a function of space and time.

5.1.5 INITIAL-TIME-DELAY GAP (TI).

This gap measures how large the hall sounds, quantifying the perception of intimacy the listener feels in a space. It depends purely on the hall’s geometry, measuring the time delay between the arrival of the direct sound and that of the first reflected wave to reach the listener. To make comparisons among different halls, records of a single value per hall, measured at a representative location in the centre of the main seating area. It is best if TI does not exceed 20ms.

5.2 INVERSE PROBLEM FORMULATION

To work with the Inverse Optimization system problems are phrased given a description of a set of desired measures for acoustic performance, determine the material properties and geometric configuration that will most closely match the target. To formulate the acoustic design process as a constrained optimization problem, the system requires a specification of;

(1) The optimization variables that express how a hall may be modified,

(2) The constraints that must be satisfied, and

(3) The objective function.

6.0 CASE STUDIES

6.1 OAKRIDGE BIBLE CHAPELOakridge Bible Chapel in Toronto, Canada, exhibited a fundamental acoustic flaw in its initial design. The walls and ceiling were faced with highly reflective plaster, which produced excessive reverberation. This caused the sound from one spoken syllable to linger and mask the following syllable. Even when sufficiently loud, speech became almost unintelligible. A simulation of the existing environment was run, which confirmed the speech intelligibility problem. Figures11 through 13 show the results of the simulation. The width of the cones and height of the bass cylinders indicate that both EDT and BR are too high. The sound strength visualization shown in Figure 13 demonstrates that the total sound level is also too high and that much of the distribution arrives late. The time distribution of sound energy also has a significant effect on speech intelligibility; the earlier the sound arrives, the better. Attempt was made to improve speech intelligibility by reducing the initially high values of EDT and BR while maintaining adequate sound levels. The objective function was built using EDT, BR, and G, which are the three measures relevant for speech and target values were set. Note that these values differ from those used to evaluate symphonic music. To improve speech intelligibility, sound-level target distributions on the seating plane was painted for three time slices: 0.08 seconds, 0.16 seconds, and total level. Having set the acoustic goals, modifiable components were selected and the range of the modifications was specified. Oakridge is typical of buildings constrained by their existing geometry, limiting redesign options. With this mind, the optimization was restricted to include only changes to materials. Two design scenarios were considered: one involving the ceiling surfaces—the most easily modifiable surfaces covering the largest contiguous area— and the second involving both the ceiling surfaces and walls. In the first scenario, the system assigned highly absorptive materials to cover the

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reflective ceiling surfaces. The resulting configuration yielded an objective value 97.5 percent closer to the set goal than the initial configuration.As desired, EDT dropped greatly to a fraction of the original value, and BR dropped significantly as well. Speech would be much more intelligible to the congregation with the resulting configuration. For the second scenario, the materials on the walls were altered. The system assigned highly absorptive materials to most surfaces, which improved the objective value by 98.2 percent. In the final configuration, the majority of the sound arrived early, resulting in improved speech intelligibility.The system in effect improved the temporal distribution of sound by increase g the percentage of the early sound and decreasing the percentage of late sound.

Figure 4: Computer model of Oakridge chapel (a) Plan, (b) Cross Section, (c) Longitudinal Section

Figure 5: : EDT, BR, and G values for initial, target, and optimized configurations of Oakridge Bible Chapel:

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Figure 6: Sound strength shown in the seating areas of Oakridge Bible Chapel

6.2 KRESGE AUDITORIUM

The second example, Kresge Auditorium, is a multipurpose auditorium at MIT, which is currently undergoing acoustic reevaluation (see Figure 14). The Institute uses Kresge Auditorium for everything from conferences to concerts. The hall doesn’t possess reconfigurable elements that would help accommodate such disparate acoustic requirements. Consequently, the auditorium suffers from too much reverberation for speech, although the reverberation is adequate for music. Another shortcoming is that the audience doesn’t feel surrounded by the sound, indicated by the IACC shells, which fail to encircle the glyph.

The average sound level G is 7.33 dB as compared with a range of between 4.0 to 5.5Db which is ideal for concert halls. However, the temporal distribution of energy is poor for speech intelligibility, with too much energy arriving late. While the hall’s acoustics will never satisfy all uses without introducing reconfigurable geometry or material elements, the intention was to consider modifications that would improve the acoustics as a whole. To reflect this, modification was made on the 13 weighted sound-level. Targets for both speech and symphonic music were painted for time slices at 0.08 seconds, 0.16 seconds, and total level. Unlike the Oakridge Chapel optimization, which was restricted exclusively to material changes, here optimization over geometry as well was included.

Since construction costs for geometric changes generally exceed costs for material changes, the optimization was separated into three passes—modifying only materials, only geometry, then materials and geometry combined—to compare the effectiveness of each. Using the visualization tools, observation was made on the pattern of sound-level accumulation as a function of time for the initial hall configuration. It was noted that the direct sound and the earliest reflections have the greatest effect. As

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variables for the first example, materials was selected for the seats, the wall at the back of the hall, and the walls of the stage shell, since reflected sound from these surfaces reaches much of the seating area. The optimization over materials took 72 seconds to converge, sampling 200 configurations. The system assigned absorptive material to the seats and stage floor, and reflective materials to the rear wall and remaining surfaces near the stage. The Materials only entry shows that EDT improved substantially, and BR nearly matched the target. While SDI improved, surface treatments was not included that would raise SDI much beyond 0.3. TI remained unchanged, since it is only affected by geometric changes. In the second example, the geometry modifications included the depth of the center stage wall and the rotation of the two sets of suspended reflector groups above the stage area . Each component could assume one of five positions, with the initial configuration indicated in red. These geometric components share the characteristic that the ratio between their size and the solid angle they span with respect to the sound source location is small. Further, these modifications wouldn’t require expensive alterations to the external shell of the auditorium. In the optimization over geometry, the system left the orientation of the rear reflector group unchanged, but lowered the forward reflector group and moved the rear stage wall to the position closest to the source. These modifications improved TI by 58 percent.

The optimization took approximately 20 minutes to converge while sampling 100 geometric configurations. The combined optimization—involving both materials and geometry—altered materials as before. However, it selected a new configuration for the banks of reflectors, raising the rear reflector group, lowering the forward reflector group, and again moving the rear stage wall to the position closest to the source. This configuration produced the lowest cost by maintaining the improvements to TI from geometry modifications and improvements to EDT from material modifications. Sound-level G dropped to 5.0 dB and the temporal distribution improved, with a higher percentage of the energy arriving earlier than in the initial configuration. IACC improved somewhat, but remained far from optimal, which is expected for fan shaped halls such as this one. The optimization took 17 minutes to converge while sampling 80 geometric configurations, improving the overall acoustic rating by 47.8 percent. The results in Table 2 and Figure 15 show that performance improved for both uses. Finally, taking the resulting geometric configuration from the combined optimization, we introduced a set of materials that could be changed between speech and symphonic music performances. Examples are curtains that could be drawn or rugs that could be taken up. We restricted our study to stage surfaces and the auditorium’s back wall. The system assigned highly absorptive materials for the speech configuration and materials with mid to low absorption for the music configuration. The interactive system for acoustic design solves a restricted inverse problem. The user provides a specification of desired acoustic performance and describes material and geometric variations and constraints for a collection of architectural components in the scene. The system then searches the design space for the configuration that

14 “best” meets the specification. This approach can be easier and more intuitive to use than the usual direct edit-simulate cycle.

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Figure 7: Eero Saarinen’s Kresge Auditorium Massachusset Institute of Technology,Cambridge

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7.0 REFERENCES

Concert Hall Acoustics (1982) The Anstendig Institute, Revised 1984.

Nuclear, Energetics and Environmental Control Engineering Dept., University of Bologna, Viale Risorgimento 2, 40136 BOLOGNA (Italy)

Ogunsote O.O (2008).’Acoustic and Noise Control’-Lecture notes Fut. Akure. (Unpublished)

Savvioja L. (1999).’’Modelling Techniques for Virtual Acoustics’’ Doctorate thesis. Helsinki University of Technology.

Tsingos N. and Carlborn I. (2002). Validation of Acoustical Simulation in the ‘Bell Labs Box’.Princceton University.

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