Boundary reflections create acoustical images that halve the radiation solid angle

Evidence

In Figure 13.1, the technical description of full spherical omnidirectional radiation is that the sound source “sees” a solid angle of 4π steradians. It is a “free field” with no surfaces to reflect or redirect the radiated sound. Placing the sound source on or in a large plane surface reduces the solid angle into which the sound radiates by half, to 2π steradians. Energy that would have traveled into the rear hemisphere is reflected forward; there is a reflected acoustical “image” of the source. Additional surfaces, positioned at right angles, reduce the solid angle by half, to π steradians, and then to π/2 steradians. The number of reflected images increases correspondingly. — Toole, Floyd E, Sound reproduction- the acoustics and…, 1455

Categorization

• DEFINE: Defines solid angle (steradians) and the acoustical-image model of boundary reflections in precise quantitative terms.