Acoustics in Architectural Design E-Book

Raf Orlowski

• Herausgeber: The Crowood Press
• Kategorie: Fachliteratur
• Sprache: Englisch

Seitenzahl: 269

Veröffentlichungsjahr: 2021

Beschreibung

It was not until the beginning of the twentieth century that the physicist Wallace Clement Sabine developed his theory of reverberation, which has remained fundamental to architectural acoustics to this day, and has subsequently been applied to many building types, especially those for the performing arts. Yet the practice of architectural acoustics goes back much further with the impressive designs of the Greeks proving highly influential. This comprehensive book explores the development of acoustics in architectural design from the theatres of Classical Greece, through the early development of opera houses, concert halls and theatres, to the research work of Sabine and his successors and its influence on twentieth- and twenty-first-century buildings. Topics covered include: the fundamentals of acoustics; the influential legacy of the Greeks and Romans; the evolving design of opera houses, theatres and concert halls and, finally, the acoustics of schools, music schools and recital halls.

Leseprobe

Acoustics

IN ARCHITECTURALDESIGN

Acoustics

IN ARCHITECTURALDESIGN

First published in 2021 byThe Crowood Press LtdRamsbury, MarlboroughWiltshire SN8 2HR

[email protected]

This e-book first published in 2021

© Raf Orlowski 2021

All rights reserved. This e-book is copyright material and must not be copied, reproduced, transferred, distributed, leased, licensed or publicly performed or used in any way except as specifically permitted in writing by the publishers, as allowed under the terms and conditions under which it was purchased or as strictly permitted by applicable copyright law. Any unauthorised distribution or use of this text may be a direct infringement of the author’s and publisher’s rights, and those responsible may be liable in law accordingly.

British Library Cataloguing-in-Publication DataA catalogue record for this book is available from the British Library.

ISBN 978 1 78500 879 5

Cover design by Sergey Tsvetkov

Contents

Introduction

Chapter OneFundamentals of AcousticsChapter TwoOpera Houses and Concert Halls (Pre-Twentieth Century)Chapter ThreeOpera Houses and Concert Halls (Twentieth to Twenty-First Centuries)Chapter FourThe Acoustics of TheatresChapter FiveThe Acoustics of SchoolsChapter SixMusic Schools and Recital HallsChapter SevenOther Building Types

Conclusion: Future Possibilities

Glossary of Acoustical Terms

Acknowledgements

References

Index

Introduction

THE FRENCH ARCHITECT, LE CORBUSIER, regarded as one of the fathers of modernism, is quoted as saying that ‘Architects have a feeling for space’. He could have said the same thing about acousticians, although he would have been talking about quite a different perception of space. Architects sense space by visual cues, whilst acousticians sense space by aural cues. This difference was highlighted rather starkly in a lecture course to architecture and engineering students by Robert E. Apfel at Yale University, which was entitled ‘Deaf architects and blind acousticians’.

This sensing of space using aural cues goes right back to the Stone Age, where people explored tunnels and caves in the dark and made noises to find spaces that were more resonant or reverberant. When they located such spaces they painted pictures on the walls, which are still evident today, and it is suggested that some of these caves may have been used for rituals or initiation ceremonies.

The beginnings of the understanding of acoustics can be traced back to the sixth century BC, when it is thought that the Greek mathematician Pythagoras had worked out that sound is a vibration transmitted from a source to the ear. In fact the word ‘acoustics’ comes from the Greek akoúō, which means ‘to hear’.

The Greeks went on to build some spectacular theatres, the most famous of which is the theatre at Epidaurus, built in the fourth century BC. It is still in existence today, and is reputed to have excellent acoustics – it will be discussed in more detail in Chapters 1 and 2.

The Romans followed on from the Greeks in building theatres, and in the first century BC the Roman architect Vitruvius documented the principles of theatre design is his Ten Books of Architecture. This is a very important document, as it not only tells us the Roman approach to building theatres, including ideas on acoustics, but it influenced the resurgence of theatre construction in the Renaissance period.

Leading Renaissance architects such as Palladio were influenced by Vitruvius’ writings: this is evident in the plan shapes they designed, which are based on the amphitheatre model (Palladio’s theatre, the Teatro Olimpico, is discussed in Chapter 4). These amphitheatre-type designs later developed into the horseshoe plan shape typical of opera houses in the eighteenth and nineteenth centuries, a tradition that continues into the twenty-first century.

In terms of acoustics, little progress was made in developing the science of architectural acoustics before the twentieth century. The Italian architect, Niccolini, designer of the Teatro San Carlo in Naples (1817), wrote ‘Until the present day, the nature of sound propagation is considered by many as an unknown mystery.’ Even in the late nineteenth century the subject was still largely considered a mystery. The eminent Viennese architect Adolf Loos published an essay in 1912 entitled Das Mysterium der Akustik, in which he said that concert halls become acoustically excellent when fine music played in them is gradually absorbed by the walls. In the mortar, he said, live the sounds of the great composers. But brass instruments, he warned, have a bad effect, and military music can ruin the acoustics within a week.

The breakthrough in architectural acoustics came at the turn of the twentieth century when Harvard professor, Wallace Clement Sabine, developed his theory of reverberation and effectively became the father of modern architectural acoustics. Sabine proposed the concept of ‘reverberation time’ (RT), which is approximately the time it takes in seconds for a loud sound in a room, when stopped, to decay to inaudibility. He showed that reverberation time is linked to intelligibility of speech – short RTs give good intelligibility, whilst long RTs make speech less clear.

He showed that reverberation time is directly proportional to the volume of a room, and inversely proportional to the total acoustic absorption. Sabine’s equation, which is seductively simple, has profoundly influenced room acoustics throughout the twentieth century, and continues to do so in the twenty-first. Further details of the equation and examples of its use are described in Chapter 1.

Following Chapter 1, which provides an introduction to the fundamentals of acoustics, the book proceeds to look at the relationship between acoustics and the architectural design of various building types. Starting with the design of auditoria, which is perhaps where acoustics is particularly prominent, a description is given of the evolution of auditoria for opera, music and theatre. This is followed by the acoustic design of schools, which, relatively recently, has been influenced by regulation in England and Wales in a highly beneficial way. Other building types then follow, such as worship spaces, law courts, museums, transportation buildings, and open plan offices.

This book should be of interest to architecture students and their qualified colleagues, musicians, theatre consultants, acousticians, building engineers, and those who procure and manage buildings where acoustics is of fundamental importance.

Chapter One

Fundamentals of Acoustics

Definitions of Sound

An early definition of sound comes from the Roman architect, Vitruvius, who lived in the first century BC. In his writings on architecture, contained in The Ten Books of Architecture (translated by M.H. Morgan, 1960), he wrote the following description about the nature of sound produced by the voice:

Voice is a flowing breath of air, perceptible to the hearing by contact. It moves in an endless number of circular rounds, like the innumerably increasing circular waves which appear when a stone is thrown into smooth water … but while in the case of water the circles move horizontally on the plane surface, the voice not only proceeds horizontally, but also vertically in regular stages.

Fig. 1.1 Circular waves when a stone is thrown into still water. (Photo: Alamy)

This is a useful definition as it enables us to picture sound waves travelling outwards from a source as a series of expanding concentric spheres (Fig. 1.1). As the distance from the source increases, the amplitude of the waves will gradually diminish.

Another, more modern definition, is that sound is a disturbance that propagates in an elastic medium, such as air, at a speed that is characteristic of that medium. This establishes that the speed of sound is constant in air. In fact it is 343m/sec at 20°C. The variation with temperature is very small, so this is not a concern in architectural acoustics. The term ‘disturbance’ in the above definition usually means there is a vibrating object, such as a vibrating tuning fork or a loudspeaker diaphragm, which is compressing and expanding the air adjacent to it and hence generating sound waves.

A third definition is that sound is a sensation perceptible to the human and animal hearing systems. The nature of the human hearing system will be discussed a little later.

Wavelength and Frequency

Fig. 1.2 illustrates the sound wave of a pure tone such as a steady whistle. The vertical axis represents pressure, and the waveform shows variations in air pressure relative to atmospheric pressure. These variations are very much smaller than the atmospheric pressure itself. The horizontal axis represents time or distance from the source. The first part of the wave shows a steady increase in air pressure from zero to a maximum, followed by a steady decrease back down to zero. This part of the wave is called a compression. The second part of the wave shows a decrease below atmospheric pressure down to a minimum, which then rises back to zero. This is called a rarefaction. The cycle then repeats itself. So a sound wave basically consists of a series of compressions and rarefactions.

Fig. 1.2 Sound wave of a pure tone.

Fig. 1.3 High frequency sound wave (a, above) relative to low frequency sound wave (b, below).

If the number of cycles of the sound wave occurs more quickly in a given time period than in Fig. 1.2, the pitch of the sound increases. Conversely, if fewer cycles occur, the pitch of the sound decreases. This is illustrated in Fig. 1.3.

The number of cycles occurring in one second is referred to as the frequency of the sound which has the unit hertz (Hz). So, for example, the middle C note on a piano generates 262 cycles per second, or 262Hz.

The other key parameter of the wave in Figs 1.2 and 1.3 is the distance between repetitions – this is referred to as the wavelength, and is measured in metres. Sound waves obey the same rules as other wave motions, where the fundamental relationship is:

As the speed of sound in air is constant, then the frequency is inversely proportional to the wavelength; this means that as the frequency increases, the wavelength decreases, and vice versa.

It is useful to know the range of wavelengths occurring in architectural acoustics. The wavelength of the middle C note on the piano is 1.3m. The lowest note on a bass guitar or double bass, which has a frequency of 40Hz, has a wavelength of 8.6m. By contrast, the highest note on a piccolo, which has a frequency of 4,000Hz, has a wavelength of 0.086m, or 8.7cm.

The relationship between the wavelengths of sound and the dimensions of rooms, buildings and other constructions in the built environment is very relevant.

Fig. 1.4 The effect of a barrier at different sound frequencies.

For example, consider a tall fence, say 2.5m (8ft) high, alongside a motorway: the road traffic noise will be quieter on the far side of the fence but remains audible because the sound waves bend around the top of the fence; this bending effect is called ‘diffraction’. As well as being quieter on the far side, the quality of the sound will be different: it will be more of a ‘rumble’ without the ‘hiss’. This is because long waves (low frequencies) bend easily around obstacles, whereas short wavelengths (high frequencies) bend very little and create a shadow zone. This is illustrated in Fig. 1.4.

In general, long waves bend around most obstacles and continue along their path, whereas short wavelengths create a shadow zone because they bend very little.

Now consider sound in a room: if the wavelength of the sound is the same as one of the room dimensions, say the distance between two parallel opposite walls, then the sound energy in the wave will become trapped between the two surfaces and will oscillate backwards and forwards forming a resonance – rather like an organ pipe. These resonances are called standing waves, and the sound energy in them can persist longer than other sound reflections in the room. The effect is most obvious in small rooms, and is one of the reasons why singing in a bathroom can sound very effective when these strong resonances are hit upon!

Standing waves also occur when two waves, three waves, four waves and so on fit into a room dimension. They also occur in each of the three main room dimensions, and even in the diagonals of the room. So for a room of any given size, there will be a number of frequencies where standing waves will be formed, and at these frequencies the sound will be accentuated and will tend to persist longer than other sounds.

The number of standing waves, or normal modes as they are sometimes called, in a typical room will be very large, and when the room dimensions are at least as large as the wavelength of the lowest frequency of sound, say 10m (33ft), then the modes are closely spaced in frequency and no particular sound will become prominent. However, in small rooms, normal modes are spaced more widely at low frequencies, and then individual frequencies can be strongly accentuated. This is particularly the case if two or more of the room dimensions are the same, or related by simple ratios such as 2:1.

This can be a particular problem in rooms where it is important to preserve the true quality of the sound, such as music practice rooms and recording studios. In the design of such rooms it is important to avoid the same room dimensions or simple ratios of dimensions so as to avoid strong standing waves, which could distort, or colour, the sound.

Measuring Levels of Sound: The Decibel

The range of sound pressures to which the ear is sensitive is very large, over one million to one. If these sound pressures were to be measured in standard units of pressure – namely, pascals – then the quietest sound that can be heard would be around 0.00002 pascals (Pa) or 20 micropascals (μPa) – this is generally considered to be the threshold of hearing. At the other end of the scale, one of the loudest sounds that can be heard has a sound pressure of 20Pa – this is around the threshold of pain when ‘tingling’ starts to occur in the ears. So using pascals to measure sound pressure would lead to a very inconvenient set of numbers. It would be much easier to have a scale such as the centigrade scale for temperature, which has a hundred divisions.

As a first step, it is useful to express any particular sound pressure as a ratio with reference to the quietest sound we can hear. This reference is taken to be 20μPa at 1000Hz, and forms an international standard. However, using this ratio still leaves us with a range of around a million numbers.

Instead of using unit increases in sound pressure, if we considered the number of factors of 10 increase, this would considerably reduce our range of numbers. This calculation is done simply by taking the logarithm of the number to base 10.

Fig. 1.5 Visual depiction of Weber-Fechner Law.

This concept correlates reasonably well with the way our ears perceive different levels of sound pressure. They do not respond equally to equal changes in sound pressure, but rather they respond to a given sound pressure by relating it to the sound pressure they were already hearing. This psychoacoustic effect is true not just for sound but for other senses, and is referred to as the Weber-Fechner law (Yost 2000). An example can be shown visually by viewing the two pairs of boxes in Fig. 1.5.

In the left-hand pair, the lower box has ten more dots, and it is clear that a substantial increase in dots has occurred. In the right-hand pair, the lower box also has ten more dots but this is not clearly evident. The lower right-hand box would require one hundred additional dots to be perceived as the same increase. This is, in fact, a logarithmic relationship, and one that should be followed in developing a scale for perceived levels of sound pressure.

A logarithmic unit was already available for measuring the power loss along telephone lines and was named the bel, after Alexander Graham Bell, the inventor of the telephone. However, this unit dealt with power rather than voltage (voltage in electrical terms can be considered equivalent to pressure in acoustical terms), and to adopt this unit the values of sound pressure would have to be squared, as power is proportional to pressure squared. To evaluate the sound pressure in bels, the relationship is as follows:

This provides a range of numbers according to the following calculation:

This now turns out to be a very small range of numbers to cover the very loudest sounds to the very quietest. Therefore it was decided to multiply the bel by a factor of 10 and call it the decibel (abbreviated dB). This now provides a range of numbers from 0 to 120, which has proved highly suitable for measuring the sound pressures in the human hearing range.

The key equation is:

Note that whenever the term ‘level’ is included after ‘sound pressure’ – that is, ‘sound pressure level’ – this means that the decibel scale is being used.

Examples of using the decibel scale are as follows. If the sound pressure is doubled, this results in an increase of sound pressure level of 6dB. This is a clearly audible change. By contrast, if the sound pressure is increased by around 12 per cent, the increase in sound pressure level is 1dB: this change is just about audible to the attentive listener. An increase in sound pressure of 40 per cent gives an increase in decibels of 3dB; this is considered to be an audible change in most circumstances. An approximately three-fold increase in sound pressure equates to around a 10dB increase; this is considered subjectively as a doubling of loudness.

In subjective terms, the above examples are approximations, but are useful when making general observations. It is necessary to be aware of the type of signal being listened to, in particular its spectral content, as the ear has different sensitivities to different frequencies of sound.

The Response of the Ear

It has already been said that at 1000Hz, the ear can just perceive a sound pressure of 20μPa (equivalent to 0dB). The ear is slightly more sensitive in the frequency range 3000Hz to 5000Hz, by about 4dB. However, as the frequency lowers, the ear gets progressively less sensitive, so that at 125Hz the ear is around 20dB less sensitive. So the ear has a very uneven response to different frequencies of sound: in essence it is less sensitive to low frequency sound compared with mid and high frequency sound; it is also a bit less sensitive to very high frequency sounds. However, as the loudness of sound increases, this unevenness in sensitivity becomes less pronounced, so that with very loud sounds, such as those that might be experienced at a rock concert, the sensitivity to different frequencies becomes almost the same.

Fig. 1.6 Equal loudness curves.

These different responses of the ear can be represented on a graph as a series of curves, each curve representing the sensitivity of the ear to different frequencies, and also at different levels from the threshold of hearing to the threshold of pain. These are called equal loudness curves and are shown in Fig. 1.6. The loudness along each curve remains the same, although the sound pressure level varies because of the variation in the sensitivity of the ear to different frequencies; each curve is referred to as a number of phons where the value of the phon corresponds to the sound pressure level at 1kHz.

Fig. 1.7 Frequency and sound level ranges of speech and music.

It is interesting to compare the range of human hearing with the range of speech and music; this is shown in Fig. 1.7. Note that music has a significantly greater range than speech.

When measurements of sound are made, it is useful to have a single number that correlates with the way the ear perceives the loudness of a sound. A measurement microphone will usually have a constant response to the range of frequencies audible by the human ear, and so will not replicate the insensitivity of the ear to low frequencies and very high frequencies. To do this, an electronic filter is introduced after the microphone, which mimics the response of the human ear. This filter cannot mimic the different responses at different sound levels, and so a standard filter curve has been adopted based on the equal loudness curve at a level of 40 phons.

Fig. 1.8 A-weighting curve.

The response of this filter is shown in Fig. 1.8, where it can be seen that the filter reduces the signal gradually as the frequency decreases, in the same way that the ear does. The frequency weighting of this filter is termed an A-weighting, and sound levels measured with this filter are denoted as dBA.

Fig. 1.9 Typical sound pressure levels. (Copyright © Brüel & Kjær)

It is useful to consider everyday sounds in terms of their sound levels in dBA. These are set out in Fig. 1.9. Note that it is very rare to experience sound levels below 20dBA as this requires ambient noise such as road traffic and birdsong to be excluded from a space; broadcast studios and concert halls can have such low sound levels.

When considering acoustics in engineering terms – where, for example, there might be a need to reduce the noise of a large ventilation fan – a single figure number in dBA is not sufficient to implement noise-control measures, such as specifying a silencer. It is necessary to consider the noise of the fan at different frequencies, and to do this, the frequency spectrum is divided into bands that cover the audible spectrum.

Fig. 1.10 Sound spectrum divided into octave bands.

The convention that has been adopted for these frequency bands is that they are divided into octaves where the uppermost frequency in each band is twice the lower frequency. (These octaves are the same octaves as used in music.) Furthermore, the positioning of the octave bands in the frequency spectrum follows an international standard where each band is referred to by its centre frequency. So around the centre of the spectrum there is the 1000Hz band, and below this there is the 500Hz band, 250Hz band, 125Hz band and so on. Above 1000Hz, there are the 2000Hz, 4000Hz bands and so on. These octave bands are shown in Fig. 1.10.

For more detailed analysis, each octave band can be split into three third-octave bands, and for even finer analysis, narrower bands can be used, which is termed narrow-band analysis.

Elements of Room Acoustics

In introducing room acoustics, it is useful to first consider sound outdoors as might have been experienced in a traditional Greek theatre such as the one at Epidaurus (Fig. 1.11). This theatre is dealt with in more detail in Chapter 2, but serves here as a useful introduction.

Fig. 1.11 Epidaurus amphitheatre (a) and plan (b).

Fig. 1.12 Direct sound and reflection at Epidaurus (a), and the resulting impulse response (b).

The speech sounds from an actor on the stage of the Greek theatre will reach a listener first by the direct path, as shown in the section in Fig. 1.12; this is called the direct sound. Very shortly afterwards, the listener will receive a repetition of the direct sound via a reflected path where the reflection is from the stage: this is called an early reflection.

If we wanted to record the acoustic characteristics between the speaker and listener in the theatre, we could make an impulsive sound at the location of the speaker, such as a hand-clap or gun shot, and measure the response at the location of the listener. This response would look like the plot adjacent to the section where we can see the direct pulse arriving at the listener, followed by a second pulse that is smaller in amplitude because it has travelled further and also lost some energy on reflection. This type of plot is very important in room acoustics, and is called an impulse response – it shows the sequence of reflections following the direct sound and their time delays.

Fig. 1.13 Sound reflections in a room (a) and the resulting impulse response (b).

Considering now the sound between speaker and listener in a more conventional theatre with a roof, there are now not one, but a multitude of reflections following the direct sound. These reflections are generated by the ceiling, the walls, and all the other surfaces and objects in the theatre, as shown in Fig. 1.13. If the impulse response is measured between speaker and listener in this space, it is much more complex than in Greek theatre, as shown in the associated plot.

This impulse response can usefully be divided into two parts: the first part includes the direct sound and early reflections, and these early reflections are generally considered to arrive within a tenth of a second of the direct sound. In the second part, the reflections become much denser, and gradually diminish in amplitude; these reflections are called late reflections or reverberation.

In listening to sound in a room, it is clear that each individual reflection is not heard, otherwise there would be a cacophony of sound. The ear and brain integrate the early reflections with the direct sound, and this adds to the loudness of the direct sound and enhances overall clarity. The later reflections are heard as a reverberant decaying tail, referred to as ‘reverberation’. The balance between early and late reflections is fundamental to the quality of the sound that we hear.

Reverberation

The length of the reverberation in seconds depends on the type of room being considered: in a cathedral the reverberation can be very long, up to 10 seconds or more, whereas in a typical domestic living room it will be around 0.5 seconds.

Fig. 1.14 Comparison of sound decays in a concert hall and a church.

When listening to speech or music in a room, each individual syllable or note will have a reverberant tail, and if the reverberation is long, as in a cathedral, this tail will run into the next syllable or note and will mask it to some extent, making speech difficult to understand and music indistinct. This is depicted in the lower diagram in Fig. 1.14.

By contrast, if the reverberation time is short, each syllable or note will stand out more clearly, and the tail will impinge less on its neighbour; this is shown in the upper diagram – in this case speech will be clear and music distinct.

However, there are different requirements for speech and music: speech requires a shorter duration of reverberation than music to provide good intelligibility, whereas in music the notes need to flow into each other to a certain extent. So there is an optimum value for the duration of reverberation for speech, which is around 1 second and an optimum one for music, which is typically around 2 seconds (depending on the style of music).

The duration of reverberation is called the ‘reverberation time’, and the theory of reverberation was developed at the turn of the twentieth century by a Harvard professor, Wallace Clement Sabine.

Fig. 1.15 Plan and section of the lecture theatre at the Fogg Art Museum.

Sabine’s work on reverberation was initiated at Harvard University because a new lecture theatre, housed in the Fogg Art Museum, had quickly gained a reputation for very poor acoustics for speech. The lecture theatre, opened in 1895, was designed according to the classical Greek form, and is shown in plan and section in Fig. 1.15. The President of the University invited Sabine, an assistant physics professor at the time, to investigate the problem and to come up with a solution. This led to a fundamental breakthrough in architectural acoustics, and gave birth to the modern science of acoustics.

Sabine developed a simple method of measuring the persistence of sound based on using an organ pipe and a stop watch. He found that the reverberation time in the empty lecture theatre was 5.5 seconds. Sabine explained the problem of this long reverberation time as follows:

During this time [reverberation time] even a very deliberate speaker would have uttered the twelve or fifteen succeeding syllables. Thus the successive enunciations blended into a loud sound, through which and above which it was necessary to hear and distinguish the orderly progression of the speech. Across the room this could not be done; even near the speaker it could be done only with an effort wearisome in the extreme if long maintained. (Sabine 1922)

Sabine then proceeded to install lines of cushions into the lecture theatre, and measured the reduction in reverberation time at each stage. He found that by installing cushions on all the seats, the aisles, the platform and the rear wall, the reverberation time was reduced to 0.75 seconds. He also found that the graph plotting the reverberation time against the amount of acoustic absorption was a rectangular hyperbola. He thus showed that reverberation time is inversely proportional to the amount of absorption.

Sabine repeated his experiment in rooms of different sizes and further found that the reverberation time is proportional to room volume. He thus came up with the most fundamental relationship in architectural acoustics, which relates reverberation time to room volume and total acoustic absorption. He expressed this finding in his paper on the subject rather modestly, as follows:

We have thus at hand a ready method of calculating the reverberation for any room, its volume and the materials of which it is composed being known.

The relationship is quite rightly known universally as Sabine’s equation, and the underlying theory as Sabine’s theory. The equation in metric units can be written as follows:

Sabine’s equation is fundamental to room acoustics, and remains the most important method for calculating the reverberation time in a room. Calculating the volume of a room is usually straightforward, although it can be tricky with complex geometries such as sometimes occur in theatres. The total acoustic absorption is calculated by taking the area of each surface (S) in the room and multiplying it by its absorbing power (the absorption coefficient of the material (α) – see next section for definition) giving S α. Then the absorptions of all the surfaces are added together, giving the total absorption, A:

As an example, a simple calculation can be carried out of the reverberation time of a concert hall. It is assumed that the concert hall is shaped like a large shoebox with length, width and height dimensions of 36 × 20 × 16m (98 × 66 × 52ft). It is further assumed that the walls and ceiling are of plastered masonry, and that the whole floor is covered by audience and orchestra. The volume of the concert hall is therefore 11,520m3 (15,068yd3) and the surface area of the walls and ceiling is 2,512m2 (3,004yd2). Assuming a sound absorption coefficient of 0.1 for the walls and ceiling (this means 10 per cent of the incident sound is absorbed), their total absorption is 251.2m2. The audience is much more absorbing and will have an absorption coefficient of around 0.9, which puts the absorption of the audience at 648m2. The total acoustic absorption in the hall is therefore 899m2. The reverberation time can now be calculated by Sabine’s equation where

This is a typical value for a concert hall for orchestral music.

Reverberation time is measured following the international standard procedure: namely, to determine the time taken in seconds for a sound, when stopped, to decay by 60dB.

Fig. 1.16 A typical decay curve.

Traditionally, reverberation time is measured by making a loud impulsive sound, such as a gun shot, and recording the decay of the sound level. The slope of the decay is measured using a calibrated protractor, giving an answer in seconds. An alternative method involves radiating a noise signal from a loudspeaker, which is switched off and the resulting decay recorded. Fig. 1.16 illustrates the type of decay curve that is produced, which is not totally smooth but has small fluctuations. In practice, it is not usually possible to measure the full decay over 60dB due to limitations of instrumentation, and so the measurement is taken from a point 5dB below the peak level to 35dB below (a 30dB range) – the time period measured is then multiplied by two to represent the full 60dB range.

Present-day equipment measures the reverberation time digitally and gives a numerical readout, although the decay curves can still be viewed to see if there are any irregularities. One such irregularity could be a prominent peak along the decay, which would indicate a strong echo – this could be problematic in a theatre or concert hall.