Theory of continuously phased planar sources for sound reinforcement

\nModern large-scale sound reinforcement systems use line-source loudspeaker arrays with the goal to establish a desired direct sound level decay profile along a line into the audience by adjusting the splay angles or delays between the individual enclosures. To design such a profile not only in the depth but also in the width of the audience area, a two-dimensional source would offer sufficiently many degrees of freedom for adaptation. In practical applications, this task is often accomplished with discrete planar loudspeaker arrays. In this work, we suggest employing the stationary-phase approximation to get a continuous symmetric delay length profile, which is then discretized. The aim of the design is to achieve direct sound levels rolling off by −6 ⋅ β dB per distance doubling on the listening area. The efficacy of this method is demonstrated by simulations and measurements of coverage with a small planar array confirming the validity of the proposed theory in practice.\n