Acoustic modelling

While design on the basis of rules-of-thumb and of precedent provide valuable guides, only reverbera-tion time can be predicted from architectural draw-ings, and even there cases arise when the predic-tion is inaccurate. It has now become commonplace to use some form of modelling to assist design. Tra-ditionally physical models were used but compu-ter models are gaining popularity as they become more sophisticated.

In their historical review, Cremer and Müller (1982) cite water-wave model experiments by Scott Russell as early as 1843. Similar two-dimensional studies in air were made by W.C. Sabine in 1912 using the Schlieren technique (Sabine, 1922). The value of these studies was limited though to those two dimensions. A major reason for wanting a model study is to aid with comprehension of three-dimensional behaviour. To do this, either acoustic testing in physical scale models of auditoria or com-puter analysis is necessary.

62 Acoustics for the symphony concert hall

3.9.1 Acoustic scale models

Testing acoustics in scale models dates back to work by Spandöck in the 1930s (Barron, 1983). In the intervening years the principles of modelling have remained the same but major advances have been made in equipment and latterly by the introduction of digital signal processing. The virtue of acoustic scale modelling is that the complex behaviour of sound when it meets finite-size surfaces or obsta-cles depends on the relationship between the size of the surface and the wavelength of sound. Scale modelling depends on scaling the wavelength in line with the physical scaling.

The scaling procedure is based on two funda-mental equations:

Air (or nitrogen which constitutes 80 per cent of air) is nearly always used as the propagating medium in the model so the speed of sound is the same both in the model and at full-size. Both dis-tance and time are scaled together in the model but more significantly since wavelength has to be scaled with distance, frequency must be increased.

In a 1:10 scale model, frequency is increased by a factor of 10. The particular attraction of acoustic scale modelling is that in most respects the model-ling is perfect; the same acoustic behaviour occurs in the model in miniature.

The one complication is that, due to the fre-quency transposition, absorption of sound as it travels through air becomes an issue. This phenom-enon of air absorption has already been mentioned as it influences high-frequency reverberation time (section 2.8.5). It is an effect which becomes pro-gressively more marked the higher the frequency.

The major component of the absorption, known as molecular absorption, can however be control-led since it depends on the simultaneous presence of oxygen and water vapour. The problem of air absorption in models can be almost eliminated by the use of low-humidity air (at around 2 per cent

r.h.) or by using a nitrogen atmosphere. For impulse responses, an alternative is to make corrections to recorded responses as one element of digital signal processing; unfortunately this has the disadvantage that it reduces dynamic range.

For the model itself, materials have to be used which match the absorption characteristics of full-size surfaces. To measure absorption by model materials, the same procedure is used as at full size, with a sample of material tested in a model-size reverberation chamber. It turns out that to repro-duce an auditorium is simpler than most other spaces since most surfaces are acoustically hard and can be modelled with hard smooth surfaces.

The most common model materials are varnished timber or plastic; plastic has the advantage that it contains no moisture.

The major absorbing element in an auditorium is audience seating or audience themselves. For seating upholstery, fabrics chosen by trial-and-error are generally used. It is also important to reproduce the seating physically since rows of seating scatter as well as absorb sound.

Model scales of between 1:8 and 1:50 have proved most appropriate. The traditional scales were 1:8 and 1:10; the first of these being a whole number of octaves and being suitable for tape recorders which have speeds based on factors of two (Figure 3.26). 1:10 is obviously convenient for architectural drawings. The disadvantage of the large model is the space it requires, the construction cost and the time it takes to build the model. One would not wish to base the model on the design too early in the design programme, but only having results from the model testing when the design is nearly fixed is not suitable either.

At the other extreme, modelling at 1:50 scale overcomes these problems and allows modelling to become fully integrated in the design process (Barron and Chinoy, 1979). A concert hall model at this scale will be about 1 m long (Figure 3.27). The range of measurements that can be made in small models is less than in large ones, predominantly objective rather than subjective measurements.

This comes about since the maximum measurement Speed of sound = Distance

Time

Frequency Wave length

= ×

Acoustics for the symphony concert hall 63

Figure 3.27 A 1:50 scale acoustic model of the Waterfront Hall, Belfast Figure 3.26 A 1:8 scale acoustic model of the Barbican Concert Hall, London

64 Acoustics for the symphony concert hall

frequency is around 100 kHz. Models with scale factors of 1:20 or 1:25 offer a good compromise.

The limiting measurement frequency of 100 kHz is of course well above any frequency we can hear with our ears. But it is the transducers, microphones and loudspeakers, which introduce the limit. Micro-phones with a diameter of less than 1/8 inch (3 mm) are rare, while loudspeakers for ultrasonic frequen-cies become highly directional. A very valuable sound source for models is an electrical spark dis-charge. This has the advantage that the source of sound can be very compact; the electrical energy in the spark determines the frequency of maximum acoustic energy.

Objective testing in models gives numerical values such as reverberation time, which can be compared with criteria developed at full size. A series of listener and source positions are tested. In reality a perfect match of reverberation time with prediction is rarely achieved, absorption often does not match at all measurement frequencies. Model-ling is especially valuable for the other objective quantities, such as objective clarity and total sound level, which cannot be predicted from drawings;

these can be corrected for the small reverberation-time errors that arise (Barron, 1997).

Subjective testing refers to listening to music that has been processed by the model. The tradi-tional technique was to use a multiple-speed tape recorder: speeded-up speech or music was played through the model and slowed down again to be listened to over headphones. Other more sophis-ticated techniques involving computers have also been used. For recording in a model, an accurate 1/10th scale model head has even been developed to allow realistic recordings (Xiang and Blauert, 1991). Subjective testing is a highly seductive prop-osition, offering the chance to hear the sound of a space before construction. But this opportunity should not blind one to the fact that no system like this is perfect. Using subjective testing for com-parison purposes is likely to be acceptable, but expecting to use the procedure to make an abso-lute judgement on acoustic quality of the design is probably over-ambitious.

Scale-model testing is now a mature technique for auditoria. Scale models automatically deal with the sound behaviour which is difficult to quantify, in particular scattering and diffraction at room sur-faces. Testing a model represents a small cost as a proportion of total building cost and provides much greater confidence in the acoustic behaviour.

As a design aid for major auditoria, the position of acoustic scale modelling looks secure for a while yet. Scale models have been tested to guide refur-bishment since the year 2000 of two major London concert halls: the Royal Albert Hall and Royal Festi-val Hall.

3.9.2 Computer modelling

Computer models date from the 1960s when Kroks-tad and colleagues (1968) experimented with a model based on mirror (specular) reflections using a mainframe computer. The arrival of the PC has stim-ulated the development of commercially available computer programs, many directed at auditoria.

The geometry of the hall is input and the acoustic characteristics (absorption and scattering coeffi-cients) of each surface are specified; the program calculates reverberation time and the other objec-tive measures.

The starting point for computer models is a geo-metrical model with rays or beams radiating out from a source, which are then reflected specularly at surfaces. In reality, surfaces rarely reflect specularly due to (i) surfaces being partly or highly scattering, (ii) surfaces being curved and (iii) diffraction occur-ring at reflection from finite surfaces. A fourth dif-ficulty arises because it is necessary to treat the late sound statistically (that is as a mixture of reflections) and the transition from discrete early reflections to reverberation is difficult to handle.

The magnitude of the calculation problem can be appreciated from the following. A listener in a large concert hall receives about 8000 reflections in the first second after the original sound and each reflection which arrives after a second will have undergone about 20 reflections. The time of one second should of course be seen in the context of a

Acoustics for the symphony concert hall 65 typical concert hall reverberation time of 2 seconds.

The number of sound ray impacts on surfaces that have to be considered is obviously very large, over 130000 for the one-second period after the sound is emitted. If diffusion (scattering) is included in the model, each impact of a single incident ray gener-ates several reflected rays. It is obvious that total computation time risks becoming excessive. The art of programming is to develop techniques to simpli-fy the problem in ways that do not affect anything that is significant for the ear.

At the time of writing, many computer programs include scattering and some deal efficiently with the transition from early reflections to reverbera-tion. Curved surfaces can also be handled by some programs. But the issue of diffraction remains to be tackled. The technique currently recommended for dealing with this problem is to make the geometri-cal model less detailed than one would for visual purposes. Those with experience of using computer models claim that they get reliable results using this technique. But there will always be some situations, a complex ceiling profile for instance, for which the choice of the appropriate degree of detail for the geometrical model is not obvious.

Computer models have come a long way from the early exercises on mainframe computers. Many are now using scattering coefficients, though meas-urements of these coefficients on actual surfaces are only now beginning to be published. A recent

development has been comparisons (known as round-robin exercises) in which software writers use their programs to predict acoustic behaviour of the same space (Vorländer, 1995; Bork, 2000). Only a minority of programs have been found to predict accurately.

The equivalent of subjective testing with com-puters is generally known as auralization. The procedure uses measured results on human ears, what are known as external ear transfer functions, the effects of the head on sound arriving at the two ears from different directions (Blauert, 1983). These results are used to simulate for headphone listen-ing the directions of individual reflections as calcu-lated by the computer. With all reflections treated in this way, the listener should perceive the full sound picture for a particular seat in the modelled space.

Auralization techniques are being progressively refined (Kleiner, Dalenbäck and Svensson, 1993).

Computer models are popular because they can be implemented quickly and enable acoustic con-sultants to engage with the geometrical design. The programs are cheap to use and produce elegant output that can be shown to clients; Figure 3.28 illustrates a typical rendering of a concert hall stage.

It is though the hidden part of the program that one needs to be sure of. Reliability of programs will cer-tainly increase in the coming years.

Figure 3.28 The stage area of a concert hall (Lighthouse Concert Hall, Poole) as rendered in the commercial computer simulation program CATT (courtesy of J.J. Dammerud)

66 Acoustics for the symphony concert hall