Optimal Toe-In Angle for a Dipole Loudspeaker

I’ve been doing some work on determining the best toe-in angle for a dipole loudspeaker.  The mathematical details are in this draft manuscript, but here is a brief summary.

Attenuating Lateral Room Reflections

By toeing-in a dipole one can selectively attenuate various room reflections by placing them at or near a dipole null (i.e. 90° off-axis).  Shown here are two scenarios for the first lateral reflection paths in a room, with the polar response of an ideal dipole superimposed.  Only the dipole orientation changes, the reflection paths are the same in both cases:

The first case is typical; the side-wall reflection is severely attenuated (about 30dB) since it is radiated near the dipole null.  The front reflection is helped a bit, but it’s only down 3dB (plus about 4dB due to path length).  In practice a mirror placed at the side wall reflection point will show an image of the loudspeaker on-edge. Continue reading