Below 213 Hz a living room must be analyzed by modal decay, not reverberation

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

Categorization

• QUESTION: The 213 Hz threshold for a typical living room is a concrete number worth remembering — how does it shift for other common room sizes?
• FICTION: The boundary between modal and diffuse acoustics at 213 Hz could serve as a narrative device — a room whose character changes depending on what frequency you’re thinking in.
• CANDY: Small rooms have a ‘folding point’ below which sound behaves as discrete modes — a fun fact about why small rooms sound boxy.

Related

• Modal decay analysis governs room acoustics below the critical frequency (similarity 0.93)
• Every room has a frequency below which modal effects break the diffuse-field assumption (similarity 0.87)
• Every room has a low-frequency limit below which reverberation time is meaningless (similarity 0.86)
• Room modes produce multiple decay times instead of a single exponential reverberation (similarity 0.85)
• No reverberation-time formula has universal applicability across rooms (similarity 0.84)
• A room mode’s length relative to mean free path sets its decay time (similarity 0.84)
• Every room has a low-frequency limit below which modal effects dominate (similarity 0.83)
• The diffuse field assumption underpins room acoustics predictions but fails at low frequencies (similarity 0.83)
• A single slope measurement of dB decay directly yields the reverberation time (similarity 0.83)
• A typical living room’s reverberation time rises at low frequencies, producing a boomy sound (similarity 0.82)
• A slowly-decaying frequency makes a room ring at that pitch (similarity 0.82)
• Room sound homogeneous decay holds for typical rooms but can be engineered away (similarity 0.82)
• Room size in acoustics is defined by critical frequency relative to generated sound (similarity 0.82)
• Critical distance is ill-defined in small rooms because short reverberation times fail steady state (similarity 0.82)
• Room acoustical behavior changes across a broad transition region, not at one frequency (similarity 0.82)