Wayne Parham Messages: 18791 Registered: January 2001
Illuminati (33rd Degree)
The term "waveguide" has really been taken to mean horns designed with directional control being more important than acoustic loading. Another distinction is that they don't use diffraction in the throat. See the first several pages of the document below, describing the history of CD horns and waveguides, especially around page 10.
The two criteria, constant directivity and lack of diffraction, rule out certain shapes. Exponential, tractrix and spherical horns create patterns that narrow as frequency goes up. Early CD horns provide good pattern control, but have several features that create discontinuities. The horns that can be called waveguides are generally conical (radiused at the throat if driven by a compression driver) or radial (if asymmetric, also radiused at the mouth if driven by a compression driver). An elliptical (oval mouthed) horn is similar to a radial horn, but is not a simple extrusion to make a "pie slice" with straight side walls. It maintains the flare contour at oblique angles.