Acoustic arrays of point sources

In a book on electroacoustics published in 1986, M. Rossi gives the following definition: "a network is a grouping of sources designed in such a way that its directivity corresponds to certain basic requirements".

The need to use arrays in acoustics stems from the growing importance attached to the directional characteristics of sources. This construction is necessary in many situations, both in sound recording and in sound reinforcement:

• in reverberant environments, where an increase in the directivity index results in an increase in the ratio of direct field to reverberant field and an improvement in the intelligibility of spoken messages (public address systems in stations, churches, stadiums, etc.);

• in the open field, where it is important – for efficiency purposes – to favor coverage of a given region of space (bird scaring at airports, etc.);

• in high-quality sound systems, where the aim is to maintain a homogeneous frequency response in all directions of the space to be sounded;

• in power sound systems, where the high pressure levels required call for the use of a large number of loudspeakers.

Depending on the situation, the approaches may be opposite or complementary: in some cases, the aim is to set constraints on directivity (synthesis); in others, to determine the characteristics of an existing network.

Using certain mathematical analogies with signal processing theory, this article first develops the fundamental properties of rectilinear gratings and proposes two methods for synthesizing directivity from source flow; it also specifies the limitations of these methods.

The consequences of introducing a time delay between sources are also discussed: by parameterizing the orientation and directivity selectivity of an array, it becomes possible to slave a fixed array to the position of the observation point.

The theoretical study of a circular-arc network and measurements carried out on a pair of loudspeakers then provide a better understanding of the behavior of a shape commonly used in sound reinforcement to control dispersion.

Finally, this article would not be complete if the notions of near and far fields of networks were not clarified; indeed, due to the large physical dimension of some networks, a significant part of the space covered cannot be described by the directivity function. Based on the analytical study of the field radiated by a monopole antenna, geographical limits of behavior are proposed.