INDEX

College of Santa Fe Auditory Theory

Lecture 023 Environment IV

INSTRUCTOR CHARLES FEILDING

  1. Absorption materials
  2. Porous absorbers
  3. Resonant absorbers
  4. Helmholtz absorbers
  5. Wideband absorbers
  6. Summary
  7. Diffusion materials
  8. How diffusers work
  9. Discussion
  10. Amplitude reflection gratings
  11. Sound isolation
  12. Ways of achieving sound isolation
  13. Independent partitions
  14. Flanking paths
  15. Energy-time considerations
  16. Reflection-free zones
  17. Absorption level required for reflection-free zones
  18. Brain Bullets

6.3 Absorption materials 305

Absorption materials are clearly important in their effects on the acoustics, and this section briefly looks at the factors which affect the performance of those materials and their effects on acoustic space. There are two basic forms of absorption materials-porous absorbers and resonant absorbers-which behave differently because their mechanisms of absorption are different.

6.3.1 Porous absorbers

Porous absorbers, such as carpets, curtains and other soft materials, work due to frictional losses caused by the interaction of the velocity component of the sound wave with the surface of the absorbing material. In Chapter 1 we saw that the velocity component arose because the air molecules had to move between the compression and rarefaction states. A given pressure variation will require a greater pressure gradient, and hence higher peak velocities, as the wavelength gets smaller with rising frequency. Because the pressure gradient of a sound wave increases with frequency, the friction due to interaction with a surface will also increase with frequency and therefore the absorption of these types of materials also rises with frequency. Clearly the larger the surface area available for interaction, the higher the friction and therefore the absorption. This means that porous materials which consist of a large number of fibres per unit volume, such as high-density rockwool or fibreglass, plush carpets, etc., will tend to have a high level absorption. This also explains why curtains which are draped to a fraction of their cloth area absorb more strongly than ones which are flat. A typical absorption curve for a porous absorber is shown in Figure 6.42. Because porous absorbers interact with the velocity component of the sound wave, they are affected by the space between them and the wall and their thickness. This is due to the fact that at the surface of a hard surface, such as a wall, the velocity component is zero whereas at a quarter of a wavelength away from the wall the velocity component will be at a maximum, as shown in Chapter 1, and so a porous material will absorb more strongly at frequencies whose quarter wavelength is less than either the spacing of the material from the wall, or the thickness of the material if it is bonded directly to the surface.

Fig 6.42 Typical absorption curves for porous absorbers


This effect is shown in Figure 6.43. Although in principle there could be a variation in the absorption coefficient as the frequency increases above the quarter wavelength point, due to the inherent variation of the velocity component as a function

Fig 6.43 The effect of spacing a porous absorber away from a hard surface

Fig 6.44 Typical construction of a panel absorber

of wavelength at a fixed distance from a surface, in practice this does not occur unless the material is quite thin.

6.3.2 Resonant absorbers

Resonant absorbers such as wood panelling work because the incident sound energy causes vibrations in the absorber and these are converted to frictional losses within the absorbing structure itself. This makes them sensitive to the pressure component of the sound wave and so they work well when attached to walls. The typical construction of a panel absorber is shown in Figure 6.44. In the case of wood panels it is the internal frictional losses in the wood, and in the perforated absorber, discussed later, it is due to the enhancement of velocity that happens in the perforations at resonance. Because the absorbers are resonant their absorption increases at low frequencies, as

Fig 6.45 Typical absorption curves for panel absorbers


shown in Figure 6.45. The resonant characteristics of these absorbers enables them to be tuned to low frequencies and so allows them to have absorption characteristics which complement those of porous absorbers. The peak absorption frequency of a resonant absorber is a function of the space behind the absorber and the effective mass of the front panel. To use an analogy with a spring and weight, the rear cavity acts like a spring whose stiffness is inversely proportional to the depth of the cavity and the effective mass per unit area of the front panel determines the size of the weight. As the spring gets less stiff and the effective mass becomes greater the resonant frequency drops. Thus deeper rear cavities result in lower resonances for both types. For the panel absorbers the mass per unit area of the panel is directly related to the effective mass, so heavier front panels result in a lower resonant frequency. The resonance frequency of panel absorbers can be calculated using the following equation.

fresonance = 60/sqrt(Md)

where

However, this equation must be applied with some caution because it assumes that the panel has no stiffness. This assumption is valid for thin panels but becomes less applicable as the panel becomes thicker and thus more stiff.

6.3.3 Helmholtz absorbers

Another form of resonant absorber is based on the use of the resonance that occurs when air is trapped in a tube above an air space. This type of resonance is called a Helmholtz resonance and is the resonance that occurs in a beer bottle when you blow across it. The cavity acts like a spring and the air in the tube above the cavity acts like the mass. The construction of this type of absorber consists of a perforated panel above an airspace, as shown in Figure 6.46. For the perforated panels the effective mass is a function of both the depth of the perforations and their effective area as a percentage of the total area. Their effective mass increases as the depth increases and the percentage hole area reduces. Typical absorption curves for this type of absorber are shown in Figure 6.47. This type of absorber is often used to add extra absorption at high-bass and low-midrange frequencies.

Fig 6.46 Typical construction of a Helmholtz resonant absorber.

Fig 6.47 Typical absorption curves for Helmholtz resonant absorbers.

6.3.4 Wideband absorbers

It is possible to combine the effects of porous and resonant absorbers to form wideband absorbers. A typical construction is shown in Figure 6.48 and its performance is shown in Figure 6.49. As with all absorbers using rockwool or fibreglass one must take precautions to prevent the egress of irritating fibres from the absorber into the space being treated. An alternative means of achieving wideband absorption is to use a large depth of porous absorber, for example one metre, and this can provide effective absorption with a flat frequency response, but at the cost of considerable depth.

Fig 6.48 Construction of a wideband absorber

Fig 6.49 Typical absorption curves for wideband absorbers


6.3.5 Summary

With these basic types of absorption structures it is possible to achieve a high degree of control over the absorption coefficient in a room as a function of frequency. In many cases much of the required absorption can be achieved by using materials which fit naturally in the room. For example much baroque music was performed in the halls of mansions which had a balanced acoustic due to the extensive use of wood panelling in their decoration. This panelling acted as an effective low-frequency absorber and in conjunction with the flags, drapes and tapestries which also decorated these spaces provided the necessary acoustic absorption.


6.4 Diffusion materials 311

As well as absorption it is essential that the sound be diffused when it strikes a surface. Ideally we want the acoustic equivalent of a matte surface. Unfortunately most surfaces, including large areas of absorbing material, act like acoustic mirrors, with varying shade of darkness. In order to have a matt surface one needs a 'bumpy wall' and many things can be used to provide this. Unfortunately the bumps need to be at least an eighth, and preferably a quarter, of a wavelength in size to be effective. This results in the requirement for very large objects at low frequencies, 1.25-2.5 m at 34 Hz, and very small objects at higher frequencies, 1.25-2.5 cm at 3.4 kHz. If the objects are too small, that is, less than one eighth of a wavelength, they will not diffuse properly, if they are too big, that is, greater than about a half a wavelength, they will behave as acoustic mirrors in their own right and so will not diffuse effectively. Clearly effective diffusion is a difficult thing to achieve in an ad hoc manner. Curved and angled structures can help at mid and high frequencies, and at very high frequencies, greater than about 4 kHz, the natural rough textures of materials such as brick and rough cut stone are effective. Because of the need to achieve well defined diffusion characteristics, diffusion structures based on patterns of wells whose depths are formally defined by an appropriate mathematical sequence have been proposed and used (Schroeder 1975 and D'Antonio 1984). The design of these structures is quite involved and the reader is directed to the references if they want more information. However, a brief description of how they work is as follows.

6.4.1 How diffusers work

Consider a hard surface consisting of bumps of height d. Also consider an acoustic wavefront approaching it from a normal direction. The way this wavefront is reflected will depend on the height of the bumps relative to its wavelength. Let us consider three cases:

So, one has a problem, a regular sequence of bumps will diffuse but only at frequencies at which it is an odd multiple of λ /24. Note also that these frequencies will depend on the angle of incidence of the incoming wavefront.

What is required is a pattern of bumps which alter the phases of the incident in such a way that two objectives are satisfied:

1 The sound is scattered in some 'optimum' manner.

2 The scattering is optimum over a range of frequencies.

These objectives can be satisfied by several different sequences, but they share two common properties:

Both the above properties arise because the sequences work by perturbing the wavefronts over a full cycle of the waveform. Such sequences are called phase reflection gratings because they perturb the phase of the wavefront. To make this a little clearer, let us consider two sequences which are used for diffusers.

1 Quadratic residue sequences well depth = 112 mod p where p is a prime number. If p = 5 this gives a set of well depths of:

0, 1, 4, 4, 1, 0, 1 etc.

so the sequence repeats with a period of 5.

2 Primitive root sequences well depth = a^n mod p where p is a prime and a is a suitable constant called a primitive root. For a = 2 and p = 5 we get the sequence:

1, 2, 4, 3, 1, 2 etc.

Here we have a sequence which has a period of 4 (5-1).

At the lowest design frequency for these examples a well of depth 5 would correspond to λ/2. At higher frequencies the sequences still have the same properties and thus scatter sound effectively. However, when the frequency gets high enough so that λ/2 becomes equal to the minimum difference in depths (1) then the surface again becomes equivalent to a flat surface.

The typical construction of these structures is shown in Figure 6.50 and their performance is shown in Figure 6.51.

Fig 6.50 Typical construction of a quadratic residue diffuser

Fig 6.51 Typical performance of a quadratic residue diffuser compared to a flat plate


6.4.2 Discussion

As we have seen, these sequences achieve their performance by spreading the phase of the reflected wavefront over at least one cycle of the incident wavefront. In order to do this, their maximum depth must be λ/2 at the lowest design frequency. This means that to achieve diffusion a reasonable depth is required. For example, to have effective diffusion down to 500 Hz a depth of 34 cm 03.5 inches) is required. To get down to 250 Hz one would need to double this depth. However, as we have seen, a simple bump of λ/4 can provide diffusion, albeit somewhat frequency dependently. This is half the depth of the above sequences and represents the ultimate limit for a diffusing object.

It is possible to have sequences which achieve the phase scatter required for good diffusion using a depth closer to λ/4 at the lowest frequency (4) and so allow better performance diffusers in restricted spaces. However even at low frequencies is often too large to be useful. What one really requires is a diffuser which is effective without using any depth!

6.4.3 Amplitude reflection gratings

It is not just physically observable bumps on the wall that can cause diffusion of the sound. In fact any change in the reflecting characteristics of the surface will cause diffusion. The change from an absorbing region on a wall to a reflecting one is an example of a change that will cause the sound to scatter. Thus it is always better to distribute the absorption in small random amounts around a room rather than concentrate it in one particular area. As well as encouraging diffusion this strategy will avoid the possibility that some modes might shuttle between surfaces with minimum absorption. There are also mathematically based procedures for the optimum placement of absorbing materials to encourage diffusion and more details may be found in Angus (1995). What is required is an amplitude weighting, that is, a pattern of absorbers, which gives a flat Fourier transform.

The most obvious sequences to consider are binary, that is they contain the only levels 0 and 1 where 1 represents reflection from a hard surface and 0 represents absorption from some form of absorbing material. Clearly not all acoustic absorbers are 100% absorbing but this can be simply allowed for by using (I-absorption) instead of zero in the sequence. The net effect of less than 100% absorption would be to increase the level of the specular component. Of the many possible binary sequences M-sequences would seem to be a good starting point as they have desirable Fourier properties. There are many other bi-Ievel sequences which have flat Fourier transforms but M-sequences are well documented.

Thus amplitude reflection gratings consist of a surface treatment which consists of strips of absorbing material whose width is less than λ/2 at the highest frequency of use laid out in a pattern in which strips of absorber represent zero and strips of reflecting wall represent 1 (see Figure 6.52). Note that because we are not depending on depth we do not have a low-frequency limit

Fig 6.52 Simple implimentation of a length 15 one dimensional Binary Amplitude Diffuser

Fig 6.53 implimentation of a length 1023 two dimensional Binary Amplitude Diffuser (white dots are holes drilled over absorbing material.)


to the range of diffusion only a high-frequency limit which is a function of the width of the strips. A two-dimensional example of an amplitude reflection grating is shown in Figure 6.53.

Amplitude gratings provide some diffusion but cannot be as good at diffusing as phase reflection gratings but, because of their size, they are useful at low frequencies. It also is possible to develop curved diffusion structures, although there are no simple mathematical recipes for them. For further details see Cox (1996). Other structures are possible and the reader is referred to the references for more information.

6.5 Sound isolation 316

No discussion of the quality of sound in a room would be complete without a brief discussion of how to keep unwanted sound from entering a room, or how to keep the wanted sound in, so as not to disturb the pleasure of people inside or outside it. The first thing to note is that just because a material is a good absorber of sound doesn't mean that it is a good isolator of

Fig 6.54 Sound transmission versus sound absorption in a material

sound. In fact most absorbing materials are terrible at sound isolation. This is because, in the sound isolation case, we are interested in the amount of sound that travels through a structure rather than the amount that is absorbed by it, as shown in Figure 6.54. A poor value of sound isolation would be around 20 dB which corresponds to only one hundredth of the sound being transmitted. A good absorber with an absorption coefficient of 0.9 would let one tenth of the sound through which corresponds to a sound isolation of only 10 dB! As we are more interested in sound isolations of 40 dB as a minimum, absorption is clearly not the answer!

6.5.1 Ways of achieving sound isolation

There are only two ways to achieve sound isolation, using either stiffness or mass. Figure 6.55 shows the attenuation of a partition as a function of frequency and from it one can see that stiffness is effective at low frequencies due to the fact that the sound wave must push against the stiffness of the partition. This is known as the stiffness controlled isolation region. As the frequency rises the partition needs to move less distance to reradiate a given level of sound and so it gets less effective until at the resonant frequency of the partition its level of attenuation is at its lowest value. This is due to the fact that at resonance the partition can be moved easily by the incident sound wave and so re-radiates the sound effectively. As the frequency rises above the partition's resonant frequency, the mass-controlledregion of isolation is entered.

Fig 6.55 Sound transmission as a function of frequency for a partition.


In this region, the fact that the sound must accelerate a heavy mass provides the isolation. Because more force is required to move the partition at higher frequencies, the attenuation rises as the frequency rises. At even higher frequencies there are resonances in which both the thickness of the partition, and the way sound propagates within it, interact with the incident sound to form coincident resonances that reduce the attenuation of the partition. Most practical partitions operate in the mass-controlled region of the isolation curve with coincident resonances limiting the performance at higher frequencies. Figure 6.56 shows the attenuation

Fig 6.56 Sound transmission versus frequency for typical partitions

of a variety of single partitions as a function of frequency. In particular note that the plaster board wall has a significant coincidence resonance. The performance of a single partition increases by 3 dB every time its mass is doubled but the coincidence resonances also move lower in frequency as well. These coincidence resonances limit the ultimate performance of single partitions. In addition the cost, and size, of single partitions get unreasonable for large attenuations.

6.5.2 Independent partitions

The solution is to have two or more partitions which are independent of each other. If the two partitions are truly independent then the total attenuation, or effective sound isolation, is the product of the attenuations of individual partitions, that is the dB attenuation is the sum of the dB attenuations of the individual partitions. In practice the partitions are not independent and the isolation is improved dramatically, but not as much as would be predicted by simply summing the dB attenuations. Coincidence resonances also reduce the effectiveness of a partition and it is important to ensure that the two partitions have different resonances. This is most easily assured by having them made with either a different thickness, or a different material. As an amusing example Figure 6.57 shows the measured results, from Inman (1994), for single and double glazing made with similar and different thicknesses of glass and spacing.

Fig 6.57 Sound transmission versus frequency for single and double glazing.

Because of the effect of the coincidence resonances the double glazed unit with 4 mm glass is actually worse than a single pane of 4 mm glass! As the other two curves show if the glass is dissimilar the result is much improved, and is further improved if the spacing is increased so as to reduce the coupling between the individual partitions. Often absorbing material is placed in the cavity between the two partitions to reduce the effect of coincidence resonances but it is important to ensure that the absorbing materials do not make contact with both partitions or else flanking may occur.

6.5.3 Flanking paths

Flanking paths, which are the main limitation to sound isolating structures, arise when there are other paths that the sound can travel through in order to get round, that is flank, the sound isolating structure, as shown in Figure 6.58. Typical paths for flanking are the building structure, heating pipes, and most commonly ventilation systems or air leaks. The effect of the building structure can be reduced by building a 'floating room', as shown in Figure 6.59, which removes the effect of the building structure by floating the room on springs away from it. In practice ensuring that no part of the building is touching the floating room by any means (plumbing pipes and electrical wiring conduits are popular offenders in this respect), is extremely difficult. The effect of ventilation systems and air leaks are also a major source of flanking in many cases. In fact in the domestic situation the sound isolation is almost entirely dominated by air leaks and draught paths, and it is the removal of these that allow double glazing salesmen to advertise a dramatic improvement in sound isolation, despite having two 4 mm panes of glass in the double glazing.

Fig 6.58 Flanking paths in a structure

Fig 6.59 Floating Room Construction


So in order to have good sound isolation one needs good partitions and an air-tight, draught-free, structure. Achieving this in practice while still allowing the occupants to breathe is a challenge.

6.6 Energy-time considerations 321

The main advances in acoustical design for listening to music have arisen from the realisation that, as well as reverberation time, the time evolution of the first part of the sound energy build up in the room must be considered. There are now acoustic measurement systems that can measure the energy time curve of a room directly, thus allowing a designer to see what is happening, rather than relying on a pair of 'golden ears'. An idealised energy-time curve for a room is shown in Figure 6.60 and it has three major features:

 

Fig 6.60 Idealized energy-time curve

6.6.1 Reflection-free zones

These conditions apply to the design of concert hall and, to a lesser extent, the design of the part of the studio that the musicians play in. However for the home listener, or sound engineer in the control room of a studio, the ideal would be an acoustic which allows them to 'listen through' the system to the original acoustic that the sound was recorded in. Unfortunately the room in which the recorded sound is being listened to is usually much smaller than the original space and this has the effect shown in Figure 6.61. Here the first reflection the listener hears is due to the wall in the listening room and not the acoustic space of the sound that has been recorded. Because of the precedence effect this reflection dominates and the replayed sound is perceived as coming from a space the size of the listening room which is clearly undesirable. What is required is a means of making the sound from the loudspeakers appear as if it is coming from a larger space by suppressing the early reflections from the nearby walls, as shown in Figure 6.62.

Fig 6.61 The effect of a shoter initial time delay gap in the listening room

Fig 6.62 Maximising the initial time delay gap by supressing early reflections


One way of achieving this is to use absorption, as shown in Figure 6.63. The effect can also be achieved by using angled or shaped walls. This is known as the reflection-free zone technique because it relies on the suppression of early reflections in a particular area of the room to achieve a larger initial time delay gap. This effect can only be achieved over a limited volume of the room, unless the room is made anechoic which is undesirable. The idea is that by absorbing, or reflecting away, the first reflections from all walls except the furthest one away from the speakers, the initial time delay gap is maximised. If this gap is larger than the initial time delay gap in the original recording space, the listener will hear the original space, and not the listening room. However this must be achieved while satisfying the need for even diffuse reverberation and so the rear wall in such situations must have some explicit form of diffusion structure on it to assure this. The initial time delay gap at the listening position should be as large as possible, but is clearly limited by the time it takes the sound

Fig 6.63 Achieving a reflection free zone using absorption


to get to the rear wall and back to the listener. Ideally this gap should be about 20 ms but it should not be much greater or it will be perceived as an echo. In most practical rooms this requirement is automatically satisfied and initial time delay gaps in the range of 8 ms to 20 ms are achieved.

6.6.2 Absorption level required for reflection-free zones

In order to achieve a reflection-free zone it is necessary to suppress early reflections, but by how much? Figure 6.64 shows a graph of the average level that an early reflection has to be in order to disturb the direction of a stereo image and from this we can see that the level of the reflections must be less than about 15 dB to be subjectively inaudible. Allowing for some reduction due to the inverse square law, this implies that there must be about 10 dB, or IX = 0.9 of absorption on the surfaces contributing to the first reflections. In a domestic setting it is possible to

Fig 6.64 The degree of reflection supression required to assure a reflection free zone.


get close using carpets and curtains, and bookcases can form effective diffusers, although persuading the other occupants of the house that carpets or curtains on the ceiling is chic can be difficult! In a studio more extreme treatments can be used. However it is important to realise that the overall acoustic must still be good and comfortable, that is not anechoic, and that, due to the wavelength range of audible sound, this technique is only applicable at mid to high frequencies where small patches of treatment are significant with respect to the wavelength. In this chapter we have examined how the space in which the sound is reproduced affects the way we hear and have analysed various situations and examined many techniques for achieving a good acoustic environment for hearing music.

You Need to Know

Absorption materials

Absorption materials are clearly important in their effects on the acoustics, and this section briefly looks at the factors which affect the performance of those materials and their effects on acoustic space. There are two basic forms of absorption materials-porous absorbers and resonant absorbers-which behave differently because their mechanisms of absorption are different

Porous absorbers

Porous absorbers, such as carpets, curtains and other soft materials, work due to frictional losses caused by the interaction of the velocity component of the sound wave with the surface of the absorbing material. In Chapter 1 we saw that the velocity component arose because the air molecules had to move between the compression and rarefaction states. A given pressure variation will require a greater pressure gradient, and hence higher peak velocities, as the wavelength gets smaller with rising frequency. Because the pressure gradient of a sound wave increases with frequency, the friction due to interaction with a surface will also increase with frequency and therefore the absorption of these types of materials also rises with frequency. Clearly the larger the surface area available for interaction, the higher the friction and therefore the absorption.

Because porous absorbers interact with the velocity component of the sound wave, they are affected by the space between them and the wall and their thickness. This is due to the fact that at the surface of a hard surface, such as a wall, the velocity component is zero whereas at a quarter of a wavelength away from the wall the velocity component will be at a maximum, as shown in Chapter 1, and so a porous material will absorb more strongly at frequencies whose quarter wavelength is less than either the spacing of the material from the wall, or the thickness of the material if it is bonded directly to the surface.

 

Resonant absorbers

Resonant absorbers such as wood panelling work because the incident sound energy causes vibrations in the absorber and these are converted to frictional losses within the absorbing structure itself. This makes them sensitive to the pressure component of the sound wave and so they work well when attached to walls. The typical construction of a panel absorber is shown in Figure 6.44. In the case of wood panels it is the internal frictional losses in the wood, and in the perforated absorber, discussed later, it is due to the enhancement of velocity that happens in the perforations at resonance. Because the absorbers are resonant their absorption increases at low frequencies, as shown in Figure 6.45. The resonant characteristics of these absorbers enables them to be tuned to low frequencies and so allows them to have absorption characteristics which complement those of porous absorbers. The peak absorption frequency of a resonant absorber is a function of the space behind the absorber and the effective mass of the front panel. To use an analogy with a spring and weight, the rear cavity acts like a spring whose stiffness is inversely proportional to the depth of the cavity and the effective mass per unit area of the front panel determines the size of the weight. As the spring gets less stiff and the effective mass becomes greater the resonant frequency drops. Thus deeper rear cavities result in lower resonances for both types. For the panel absorbers the mass per unit area of the panel is directly related to the effective mass, so heavier front panels result in a lower resonant frequency.

Helmholtz absorbers

Another form of resonant absorber is based on the use of the resonance that occurs when air is trapped in a tube above an air space. This type of resonance is called a Helmholtz resonance and is the resonance that occurs in a beer bottle when you blow across it. The cavity acts like a spring and the air in the tube above the cavity acts like the mass. The construction of this type of absorber consists of a perforated panel above an airspace. For the perforated panels the effective mass is a function of both the depth of the perforations and their effective area as a percentage of the total area. Their effective mass increases as the depth increases and the percentage hole area reduces.

Wideband absorbers

It is possible to combine the effects of porous and resonant absorbers to form wideband absorbers. A typical construction is shown in Figure 6.48 and its performance is shown in Figure 6.49. As with all absorbers using rockwool or fibreglass one must take precautions to prevent the egress of irritating fibres from the absorber into the space being treated. An alternative means of achieving wideband absorption is to use a large depth of porous absorber, for example one metre, and this can provide effective absorption with a flat frequency response, but at the cost of considerable depth.

Summary

With these basic types of absorption structures it is possible to achieve a high degree of control over the absorption coefficient in a room as a function of frequency. In many cases much of the required absorption can be achieved by using materials which fit naturally in the room. For example much baroque music was performed in the halls of mansions which had a balanced acoustic due to the extensive use of wood panelling in their decoration. This panelling acted as an effective low-frequency absorber and in conjunction with the flags, drapes and tapestries which also decorated these spaces provided the necessary acoustic absorption.

Diffusion materials

As well as absorption it is essential that the sound be diffused when it strikes a surface. Ideally we want the acoustic equivalent of a matte surface. Unfortunately most surfaces, including large areas of absorbing material, act like acoustic mirrors, with varying shade of darkness. In order to have a matt surface one needs a 'bumpy wall' and many things can be used to provide this. Unfortunately the bumps need to be at least an eighth, and preferably a quarter, of a wavelength in size to be effective. This results in the requirement for very large objects at low frequencies, 1.25-2.5 m at 34 Hz, and very small objects at higher frequencies, 1.25-2.5 cm at 3.4 kHz. If the objects are too small, that is, less than one eighth of a wavelength, they will not diffuse properly, if they are too big, that is, greater than about a half a wavelength, they will behave as acoustic mirrors in their own right and so will not diffuse effectively.

Curved and angled structures can help at mid and high frequencies, and at very high frequencies, greater than about 4 kHz, the natural rough textures of materials such as brick and rough cut stone are effective. Because of the need to achieve well defined diffusion characteristics, diffusion structures based on patterns of wells whose depths are formally defined by an appropriate mathematical sequence have been proposed and used.

 

Amplitude reflection gratings

It is not just physically observable bumps on the wall that can cause diffusion of the sound. In fact any change in the reflecting characteristics of the surface will cause diffusion. The change from an absorbing region on a wall to a reflecting one is an example of a change that will cause the sound to scatter. Thus it is always better to distribute the absorption in small random amounts around a room rather than concentrate it in one particular area. As well as encouraging diffusion this strategy will avoid the possibility that some modes might shuttle between surfaces with minimum absorption. There are also mathematically based procedures for the optimum placement of absorbing materials to encourage diffusion and more details may be found in Angus (1995). What is required is an amplitude weighting, that is, a pattern of absorbers, which gives a flat Fourier transform.

The most obvious sequences to consider are binary, that is they contain the only levels 0 and 1 where 1 represents reflection from a hard surface and 0 represents absorption from some form of absorbing material. Clearly not all acoustic absorbers are 100% absorbing but this can be simply allowed for by using (I-absorption) instead of zero in the sequence. The net effect of less than 100% absorption would be to increase the level of the specular component. Of the many possible binary sequences M-sequences would seem to be a good starting point as they have desirable Fourier properties. There are many other bi-Ievel sequences which have flat Fourier transforms but M-sequences are well documented.

Thus amplitude reflection gratings consist of a surface treatment which consists of strips of absorbing material whose width is less than λ/2 at the highest frequency of use laid out in a pattern in which strips of absorber represent zero and strips of reflecting wall represent 1 (see Figure 6.52). Note that because we are not depending on depth we do not have a low-frequency limit

Amplitude gratings provide some diffusion but cannot be as good at diffusing as phase reflection gratings but, because of their size, they are useful at low frequencies. It also is possible to develop curved diffusion structures, although there are no simple mathematical recipes for them. For further details see Cox (1996). Other structures are possible and the reader is referred to the references for more information.

Sound isolation

No discussion of the quality of sound in a room would be complete without a brief discussion of how to keep unwanted sound from entering a room, or how to keep the wanted sound in, so as not to disturb the pleasure of people inside or outside it. The first thing to note is that just because a material is a good absorber of sound doesn't mean that it is a good isolator of sound. In fact most absorbing materials are terrible at sound isolation. This is because, in the sound isolation case, we are interested in the amount of sound that travels through a structure rather than the amount that is absorbed by it, as shown in Figure 6.54. A poor value of sound isolation would be around 20 dB which corresponds to only one hundredth of the sound being transmitted. A good absorber with an absorption coefficient of 0.9 would let one tenth of the sound through which corresponds to a sound isolation of only 10 dB! As we are more interested in sound isolations of 40 dB as a minimum, absorption is clearly not the answer!

Ways of achieving sound isolation

There are only two ways to achieve sound isolation, using either stiffness or mass. Figure 6.55 shows the attenuation of a partition as a function of frequency and from it one can see that stiffness is effective at low frequencies due to the fact that the sound wave must push against the stiffness of the partition. This is known as the stiffness controlled isolation region. As the frequency rises the partition needs to move less distance to reradiate a given level of sound and so it gets less effective until at the resonant frequency of the partition its level of attenuation is at its lowest value. This is due to the fact that at resonance the partition can be moved easily by the incident sound wave and so re-radiates the sound effectively. As the frequency rises above the partition's resonant frequency, the mass-controlled region of isolation is entered.

In this region, the fact that the sound must accelerate a heavy mass provides the isolation. Because more force is required to move the partition at higher frequencies, the attenuation rises as the frequency rises. At even higher frequencies there are resonances in which both the thickness of the partition, and the way sound propagates within it, interact with the incident sound to form coincident resonances that reduce the attenuation of the partition.

Independent partitions

The solution is to have two or more partitions which are independent of each other. If the two partitions are truly independent then the total attenuation, or effective sound isolation, is the product of the attenuations of individual partitions, that is the dB attenuation is the sum of the dB attenuations of the individual partitions. In practice the partitions are not independent and the isolation is improved dramatically, but not as much as would be predicted by simply summing the dB attenuations. Coincidence resonances also reduce the effectiveness of a partition and it is important to ensure that the two partitions have different resonances. This is most easily assured by having them made with either a different thickness, or a different material.

Flanking paths

Flanking paths, which are the main limitation to sound isolating structures, arise when there are other paths that the sound can travel through in order to get round, that is flank, the sound isolating structure, as shown in Figure 6.58. Typical paths for flanking are the building structure, heating pipes, and most commonly ventilation systems or air leaks. The effect of the building structure can be reduced by building a 'floating room', as shown in Figure 6.59, which removes the effect of the building structure by floating the room on springs away from it. In practice ensuring that no part of the building is touching the floating room by any means (plumbing pipes and electrical wiring conduits are popular offenders in this respect), is extremely difficult. The effect of ventilation systems and air leaks are also a major source of flanking in many cases. In fact in the domestic situation the sound isolation is almost entirely dominated by air leaks and draught paths, and it is the removal of these that allow double glazing salesmen to advertise a dramatic improvement in sound isolation, despite having two 4 mm panes of glass in the double glazing.

Energy-time considerations

The main advances in acoustical design for listening to music have arisen from the realisation that, as well as reverberation time, the time evolution of the first part of the sound energy build up in the room must be considered. There are now acoustic measurement systems that can measure the energy time curve of a room directly, thus allowing a designer to see what is happening, rather than relying on a pair of 'golden ears'. An idealised energy-time curve for a room is shown in Figure 6.60 and it has three major features:

Reflection-free zones

These conditions apply to the design of concert hall and, to a lesser extent, the design of the part of the studio that the musicians play in. However for the home listener, or sound engineer in the control room of a studio, the ideal would be an acoustic which allows them to 'listen through' the system to the original acoustic that the sound was recorded in. Unfortunately the room in which the recorded sound is being listened to is usually much smaller than the original space and this has the effect shown in Figure 6.61. Here the first reflection the listener hears is due to the wall in the listening room and not the acoustic space of the sound that has been recorded. Because of the precedence effect this reflection dominates and the replayed sound is perceived as coming from a space the size of the listening room which is clearly undesirable. What is required is a means of making the sound from the loudspeakers appear as if it is coming from a larger space by suppressing the early reflections from the nearby walls

One way of achieving this is to use absorption. The effect can also be achieved by using angled or shaped walls. This is known as the reflection-free zone technique because it relies on the suppression of early reflections in a particular area of the room to achieve a larger initial time delay gap. This effect can only be achieved over a limited volume of the room, unless the room is made anechoic which is undesirable. The idea is that by absorbing, or reflecting away, the first reflections from all walls except the furthest one away from the speakers, the initial time delay gap is maximised. If this gap is larger than the initial time delay gap in the original recording space, the listener will hear the original space, and not the listening room. However this must be achieved while satisfying the need for even diffuse reverberation and so the rear wall in such situations must have some explicit form of diffusion structure on it to assure this.