Boundaries concentrate sound power but do not affect the inverse-square spreading law.

Evidence

But how does a boundary affect Equation 1.30? Clearly many acoustic contexts involve the presence of boundaries near acoustic sources, or even all the way round them in the case of rooms, and some of these effects will be considered in Chapter 6. However, in many cases, a sound source is placed on a boundary, such as a floor. In these situations, the sound is radiating into a restricted space, as shown in Figure 1.17. However, despite the restriction of the radiating space, the surface area of the sound wave still increases in proportion to the square of the distance, as shown in Figure 1.17. The effect of the boundaries is merely to concentrate the sound power of the source into a smaller range of angles. This concentration can be expressed as an extra multiplication factor in Equation 1.30. Therefore the equation can be rewritten as: where Idirective source = the sound intensity (in W m−2) Q = the directivity of the source (compared to a sphere) Wsource = the power of the source (in W) and r = the distance from the source (in m) Equation 1. — David M. Howard, Jamie Angus, Acoustics and Psychoacoustics, 312

Categorization

• QUESTION: The “directivity factor” formula being rewritten — worth confirming how the boundary geometry (floor vs. corner) maps to the solid-angle factors.
• corroborated: 2 independent passages support this claim — David M. Howard, Jamie Angus, Acoustics and Psychoacoustics, 312