Projecting a spherical wavefront onto a flat horn mouth produces a cosine roll-off.

Evidence

Secondly, the projection of the spherical wavefront’s intensity onto the planar front of the horn results in an intensity that has a cosine roll-off from the center of the horn. This approximates a Legendre weighting at the center of the planar front of the horn, as shown in Figure A6.10. Unfortunately, the weighting is not enough at the edges of the horn aperture. However, practical constant directivity horns have an additional, more extreme flare at the mouth. This would have the effect of more rapidly reducing the amplitude at the edge of the horn’s mouth; thus more closely approaching Legendre weighting. — David Howard, Jamie Angus, coustics and Psychoacoustics, 2908

Categorization

• XREF: Links the geometry of wavefront projection to the same Legendre shading function central to the CBT array discussion nearby.