Auditory Theory: Acoustics

Lecture 022 Environment III

Brain Bullets

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 of absorbers

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:
A gap between the direct sound and first reflections. This happens naturally in most spaces and gives a cue as to the size of the space. The gap should not be too long, less than 30 ms, or the early reflections will be perceived as echoes. Some delay, however, is desirable as it gives some space for the direct sound and so improves the clarity of the sound, but a shorter gap does add 'intimacy' to the space.
The presence of high level diffuse early reflections which come to the listener predominately from the side, that is lateral early reflections. This adds spaciousness and is easier to achieve over the whole audience in a shoe-box hall rather than a fan-shaped one. The first early reflections should ideally arrive at the listener within 20 ms of the direct sound. The frequency response of these early reflections should ideally be flat and this, in conjunction with the need for a high level of lateral reflections, implies that the side walls of a hall should be diffuse reflecting surfaces with minimal absorption.
A smoothly decaying diffuse reverberant field which has no obvious defects, no modal behaviour, and whose time of decay is appropriate to the style of music being performed. This is hard to achieve in practice so a compromise is necessary in most cases. For performing acoustic music a gentle bass rise in the reverberant field is desirable to add 'warmth' to the sound but in studios this is less desirable.

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.