The diffuse field assumption underpins room acoustics predictions but fails at low frequencies

Evidence

As an example, let us calculate the critical frequency of our typical living room. The second equation predicts a slightly lower critical frequency compared with the first one. However, the agreement is surprisingly good. Although the modal overlap has been calculated using a reverberation time and hence a diffuse field assumption, this is probably just valid at this frequency, which represents the boundary between the two regions. The critical frequency results show that, for this room, frequencies below 213 Hz must be analyzed using modal decay time rather than reverberation time. — David M. Howard, Jamie Angus, Acoustics and Psychoacoustics, 2038 (#expands, via linked claim)

Equation 6.16 gives us the time between surface interactions, and at each of these interactions, α is the proportion of the energy absorbed, where α is the average absorption coefficient discussed earlier. If α of the energy absorbed at the surface, then (1 − α) is the proportion of the energy reflected back to interact with further surfaces. At each surface a further proportion, α, of energy will be removed, so the proportion of the original sound energy that is reflected will reduce exponentially. The combination of the time between reflections and the exponential decay of the sound energy, through progressive interactions with the surfaces of the room, can be used to derive an expression for the length of time that it would take for the initial energy to decay by a given ratio. — David M. Howard, Jamie Angus, Acoustics and Psychoacoustics, 1830 (#qualifies, via linked claim)

Categorization

• XREF: connects to: Room sound homogeneous decay holds for typical rooms but can be engineered away; The Sabine formula assumes diffuse sound that real rectangular rooms rarely produce; Rectangular rooms fail to randomize sound directions, violating Sabine theory (+15 more)

Broader Connections

• Modal decay analysis governs room acoustics below the critical frequency #expands (0.88) — David M. Howard, Jamie Angus, Acoustics and Psychoacoustics, 2038
• Room sound energy decays exponentially through repeated surface absorptions #qualifies (0.80) — David M. Howard, Jamie Angus, Acoustics and Psychoacoustics, 1830