Acoustics in Architectural Design

Raf Orlowski

• Publisher: The Crowood Press
• Year: 2021
• ISBN:
  9781785008795
• Topic: Architecture
• Subtopic: Architecture Design

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.

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:

Speed = frequency × wavelength

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,...