Curved, Legendre-shaded line arrays exploit floor reflections to maintain constant beamwidth at all frequencies

Evidence

Figure 12.7(f) we see that shading the curved line using the Legendre contour yields a set of plots that have two desirable characteristics: a stable sound level at ear level out to 3 m or more from the loudspeaker, and a relatively constant directivity, meaning that it applies over a wide frequency range. This is a good result, and it has been called the Constant Beamwidth Transducer (CBT). This is not merely coping with the floor as an adjacent boundary, a low-frequency concern; it is using the floor reflection to create a sound field that has desirably uniform broadband sound level over a wide range of listening distances. — Toole, Floyd E, Sound reproduction- the acoustics and…, 1292

Categorization

• DEFINE: Names and characterizes the Constant Beamwidth Transducer (CBT) as a curved, shaded line source whose floor image extends the array.
• QUESTION: Why does a Hann shading contour (1290) not deliver the constant directivity that the Legendre contour achieves on the curved line — what is the psychoacoustic/cx design logic behind the specific contour choice?
• SEED: The CBT concept — using a boundary’s reflection as an acoustic extension of the transducer — is a strong story about exploiting, not fighting, room boundaries in loudspeaker design.