Speech intelligibility is a quite interesting topic, especially if one takes into consideration that early reflections support the direct sound and are necessary. However, in home cinema design and all custom home cinema installations, one would have to investigate the subject a bit further. Various authors have investigated the effect of early reflections in regards to their level and delay from the direct sound. One can derive to the conclusion that intelligibility progressively improves in home theatre applications as the delay of a single reflection is reduced and the listener would perceive a stronger ’summed’ sound.

Further investigation in small listening spaces like a home cinema room proved that the biggest issue with speech intelligibility is the signal-to-noise ratio. Noisy air conditioning systems and noise bleeding from the adjacent rooms greatly degrades the result. In other words, “more noise, less intelligible speech”.

Sabine’s equation is the equation that really started the field of quantitative room acoustics. It allows the home cinema designers to predict a crucial aspect of the acoustics of the home cinema room - its RT - if we know the volume of the room and the total amount of acoustic absorption in the home cinema. Almost as soon as we have defined this useful equation for RT, however, we run into a problem - How should the home cinema designer calculate the total acoustic absorption in a room? One simply needs to weight the absorption coefficient of each surface in the cinema room by its area and sum them. This seems to work well enough for home cinemas with RTs which are not too short. (In home cinema design, an RT prediction error of less than about 0.1 s or 10% is usually the goal.)

However, Sabine’s equation does not work so well for rooms with a lot of absorption, like a dedicated home cinema, where we expect a short RT. Consider a dedicated home cinema room where all the surfaces have an absorption coefficient of 1.0 (such as an anechoic chamber). Sabine’s equation will give a non-zero RT for such a room. This is clearly impossible, since a room with perfectly absorbing boundaries does not support any reflections at all, much less reverberation.

Predicting RT in absorbent rooms (i.e. where the RT is expected to be less than about 0.5 s), like a dedicated home cinema installation, can be done more accurately using one of the several alternative reverberation time equations. The best known of these is that due to Norris and Eyring.

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In stereo it was common to think single-mindedly of a sweet spot, and to arrange for everything to be optimum for a single listener. At low frequencies, a DSP equaliser can be used to reduce the audible excess of objectionable room resonances, thus delivering respectable bass to a single listener. However, the existence of the standing waves between and among the room boundaries ensures that other cinema seats experience different bass.

Delivering similarly good bass to everybody occupying the home cinema seating area means that the room resonances must be physically manipulated in a manner that reduces the point-to-point variations in sound pressure. Conventional acoustics attacks the problem with absorption, damping the resonances by draining energy from the offending modes, resulting in lowered pressure maxima and elevated minima. Low frequency absorption in home cinema installations is always a good idea, but it can be difficult. Traditional low-frequency absorbers were bulky devices, some of which are hostile to even progressive concepts of interior decor. They still exist, but there are some different bass-trap devices that are more elegant. The options fall into several categories, and the effectiveness of each depends on the home cinema designer’s knowledge, on where in the room to place the acoustical material or devices.

1. The modes are not absorbed as strongly as sound which visits all surfaces of a cinema room. This is due to both the reduction in the number of surfaces visited and the change in absorption due to non-random incidence.

2. This reduction in absorption is strongly frequency-dependent and results in less absorption and therefore a longer decay time at the frequencies at which standing waves occur.

3. The decay of sound energy in dedicated home cinema systems is no longer a single exponential decay with a time constant proportional to the average absorption in the room caused by the acoustic panels, etc. Instead there are several decay times. The shortest one tends to be due to the resonant modes in the home cinema room. This results in excess energy at those frequencies with the attendant degradation of the sound in the room.

The energy in a mode decay as a function of time is related to the reverberation, and the absorption in a mode has a big effect on the frequency response. This effect will be analysed separately in a future article.

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These criteria try to ascertain how significant the modal behaviour of a home cinema room is in perceptual terms. It does this by dividing the audio frequency spectrum into third octave bands, as an approximation of critical bands, and then counting the number of modes per band. If the number of modes per third octave band increases monotonically then there is a good chance that we will perceive the dedicated home cinema room as having a ’smooth’ frequency response despite the resonances.

If the number of resonances found in a home cinema installation per third octave drops as the frequency rises, then there will be a perceptually noticeable peak in the frequency response. Coincident modes are also another way of creating a perceptually noticeable frequency response peak, and the Bonello criteria do further stipulate that there should be no modal coincidence within a third octave band, unless there are at least three additional non-coincident resonances to balance the two that are coincident.

It is therefore better to choose non-commensurate ratios for the walls where a home cinema is to be installed. Proper custom home cinema design and engineering will ensure that the modes are spread out as much as possible. Much work has been done on ideal home cinema room ratios. However, the various suggested dimensions are not necessarily the only optimum ones for all room sizes. It is also important to realise that room modes are inherent in any structure which encloses the sound sources. This means that changing the shape of the home cinema, for example by angling the walls, does not remove the resonances, it merely changes their frequencies from values which are easily calculated to ones that are not.

High end home cinema installations would deal with any modal issues by using custom resonant absorbers, offering an effective modal management system in their design.

Although for low frequencies air absorbs a minimal amount of sound energy, at high frequencies this is not the case. In particular humidity, smoke particles and other impurities will absorb high-frequency energy and so reduce the level of high frequencies in the sound. This is one of the reasons why people sound duller when they are speaking at a distance.

In terms of reverberation time and also the level of the reverberation field, the effect of this extra absorption is to reduce the reverberation time in the home cinema, and the level of the reverberant field, at high frequencies above 2 kHz. Unfortunately though it is dependent on the level of humidity and smoke in the home cinema room and so the high-frequency reverberation time, and the reverberant field level, will change as the audience stays in the space. Note this is an additional dynamic effect over and above the static absorption simply due to the presence of a clothed person in the home cinema seating area, and is due to the fact that people exhale water vapour and perspire. Clearly then the degree of change will be a function of both the physical exertions of the audience and the quality of the ventilation system!

As the effect of air absorption is determined by the distance the sound has travelled (relevant to the size of the dedicated home cinema), rather than its interaction with an acoustic panel, it is difficult to incorporate the effect into the reverberation time equations. An approximation that seems to work in home cinema design is to convert the effect of the air absorption into an equivalent absorption area by scaling an air absorption coefficient by the volume of the home cinema room. This is reasonable because as the volume of the home cinema increases the more is the air that the wave must travel through, and the longer the distance that it travels. 

For home cinema installations taking place in spaces smaller than 40 cubic meters, the effect can be ignored because the equivalent absorbing area is less than 1 cubic meter. However, the effect does become significant if one is designing a large high end home cinema, and air absorption would need to be considered.

It is important that these reflections be diffuse, as specular reflections in home cinema installations will result in disturbing comb filter effects, and distracting images of the sound sources in unwanted and unusual directions. Providing diffuse reflections in custom home cinema installations is thus important and this has been recognised for some time. Traditionally, the use of plaster mouldings, niches and other decorative surface irregularities have been used to provide diffusion in an ad hoc manner.

More recently diffusion structures based on patterns of wells whose depths are formally defined by an appropriate mathematical sequence have been proposed and used, in many high end home cinema designs. However, it is not just the provision of diffusion on the side walls that must be considered when designing a dedicated home cinema room.