Las alternancias

This chapter has reviewed the relevant literature when studying the perception of room modes. A brief theoretical review has provided sources for the basic unders- tanding of the formation of standing waves, and the complex spectral and temporal responses occurring when considering a three dimensional rectangular enclosure. A number of modelling techniques have been introduced, whose implementation al- lows for detailed studies both objectively, in allowing new scenarios to be modelled, and subjectively, in that they form the basis of the auralisations used in listening tests. The modal decomposition model, with its ability to reproduce the general characteristics of a room and having efficient computation, was shown to have been used with success in low frequency psychoacoustic tests and is used in the testing throughout this thesis.

Methods by which researchers have attempted to control the low frequency sound-field have been presented systematically, from the physical design of the room dimensions, through simple absorption and more complex combinations of active control and equalisation. Importantly, it has been shown that the analysis of each of these control methods has relied upon some objective metric to determine perfor- mance. There has been very little significant study into the perceptual validity of these metrics, and this is identified as a clear research gap.

Finally, studies into the detection of individual modal parameters, such as re- sonance frequency, Q factor, and decay time have revealed some useful thresholds and trends. These include a threshold of Q of 16, and a number of exploratory studies reporting decay thresholds. However, it has been suggested that some of these are less valid in the context of real rooms with realistic music signals. It has been highlighted that overall perception, relating audible parameters and auditory sensation to an overall score, and the inclusion of perceived quality as opposed to simple affective judgements have been successfully employed to enhance the percep- tual model in fields such as surround sound, but that these techniques have not yet been implemented for characterisation of the low frequency sound-field.

Chapter 3

Low Frequency Sound Fields

3.1 Introduction

As has been shown in Chapters 1 and 2, room modes are the cause of significant audible problems, such as an excessive bass level, audible distortion and ringing at specific frequencies. It will be shown that these problems manifest themselves par- ticularly in small rooms, which this thesis considers to be between around50m3 and

250m3. This is a typical volume for rooms used as studio control rooms, mastering

studios and home listening rooms (Newell, 2007).

Chapter 2 highlighted research gaps in the area of the understanding of our perception of low frequency reproduction quality, in terms of both room and modal parameters and also overall quality. In order to understand the subjective aspects of listening within these critical listening spaces, where the sound-field is characterised by spectral, temporal and spatial elements, this chapter presents the basic theory governing the relationship between modal resonances, the physical space and the propagation of sound from a source to a receiver. Whilst this theory is not novel work, the key aspects are presented here in order to provide background and context to the interested reader.

The literature review identified a number of modelling techniques which may be used to simulate the sound-field within a room. One of these was the simple, compu- tationally efficient analytical solution commonly known as themodal decomposition. This model is derived by considering the resonant frequencies within an enclosure, the propagation from a single point source and the resulting room transfer function at a listening position. The method has been used in successful psychoacoustic re- search by Fazenda et al. (2005), Stefanakis et al. (2008a) and Welti and Devantier (2006) amongst others, and will form the basis of many of the listening tests wi- thin this thesis. As such, the derivation is presented in Section 3.3. A number of

assumptions are made when using this model which are discussed in Section 3.3.5. Section 3.4 introduces the concept of modal distribution within a room.

Finally, Section 3.5 details the use of the decomposition model in producing virtual room auralisations which may be presented to listeners over headphones during listening tests.

3.2 Modal Theory

In understanding the acoustics of enclosed spaces, it is not possible to consider sound radiation in the same terms as when radiated into free space. Therefore, such theoretical approaches as the inverse square law and the simple relationship between sound intensity and the power of a loudspeakers are no longer applicable. Rather, the sound-field is comprised of multiplemodes of vibration of the air within the room. Because of this, the distribution of sound intensity may vary widely throughout the room, regardless of the distance from the radiating source.

These modes of vibration can be described as resonances, or standing waves, but are most commonly referred to simply as room modes. It is the combination of these modes which determines the unique characteristics of a room. As with all resonances, room modes are associated with a centre frequency, known as the modal frequency oreigenfrequency. The resonance also has temporal characteristics, decaying exponentially when the sound source is removed. Finally, each mode has an associated spatial distribution, and this is known as the mode shape oreigenfunction. For a given enclosure, both the eigenfrequencies and associated eigenfunctions are derived in the following section. It must be noted that it is only possible to derive these for enclosures of certain geometries - examples being rectangular, cylindrical or spherical. This thesis considers only rectangular spaces, and in a further limitation imposed by the scope, the walls of this enclosure are considered to be smooth and perfectly rigid. This gives a boundary condition of zero particle velocity at each of the walls.