Chapter Excerpts

Chapter 12: Loudspeaker and Loudspeaker Arrays
12.15 Line Arrays

A true continuous line source is modeled as depicted in Fig. 12-71. The construction is that of an elongated cylinder of small radius wherein the radius alternately expands and contracts by a small amount about its nominal value. If the cylinder were infinitely long, this would be a source of cylindrical waves for which the attenuation rate with perpendicular distance from the cylinder would be 3 dB for each doubling of the distance.

Even with a cylinder of finite length, when observations are made in the median plane close to the cylinder this same attenuation rate is found to be true. At larger distances, however, the attenuation rate transitions to the far field value of 6 dB for doubling of distance typical of any small source having in phase surface velocity. The distance at which the far field begins depends on both the length of the continuous line source and the operating frequency. A simple analysis provides an insight on where the far field begins. Consider the situation depicted in Fig. 12-72.