Spatially proportional room dimensions create coincident resonant modes

Evidence

For a modest hall 15.76 x 20.7 x 11.76 m, there is on average one mode per Hz near 20 Hz, 14 modes per Hz at 100 Hz, and 1200 modes per Hz at 1000 Hz. The first term dominates as f grows, so the density of modes increases approximately as the square of the frequency. — Eric J. Heller, Why You Hear What You Hear- An…, 2435 (#complicates, via linked claim)

Categorization

• XREF: connects to: Linear superposition lets separate vibrations coexist independently while interfering in shared space; Hard-walled rooms behave as three-dimensional resonators with many audible modal frequencies — Ville Pulkki, Matti Karjalainen, Communication Acoustics- An…, 291; Axial mode frequencies are computable from room dimensions by a simple formula (+7 more)

Related

• Room mode density rising smoothly with frequency signals good acoustics (similarity 0.93)
• Room modes are determined by the linear dimensions of opposing surfaces (similarity 0.91)
• Axial mode frequencies are computable from room dimensions by a simple formula (similarity 0.91)
• Hard-walled rooms behave as three-dimensional resonators with many audible modal frequencies (similarity 0.90)
• Avoiding commensurate room dimensions prevents overlapping modal frequencies that cause acoustic problems (similarity 0.88)
• Spatially static resonant modes cause sound level to vary across a room (similarity 0.88)
• Three-dimensional rooms yield denser mode distributions at higher frequencies (similarity 0.85)
• Rectangular rooms are preferred because their modes are predictable (similarity 0.84)
• Dimensionally symmetrical rooms are acoustically asymmetrical due to construction details (similarity 0.84)
• Rectangular rooms allow predicting low-frequency modal behavior in advance (similarity 0.84)
• Every room has a low-frequency limit below which modal effects dominate (similarity 0.83)
• Room acoustical behavior changes across a broad transition region, not at one frequency (similarity 0.83)
• Axial room modes can be predicted from room dimensions alone (similarity 0.82)
• Exciting multiple room modes instead of one reduces frequency and spatial sound variation (similarity 0.82)
• Non-parallel walls do not eliminate room modes (similarity 0.81)

Broader Connections

• Room modes are determined by the linear dimensions of opposing surfaces #expands (0.95)
• Room modal frequencies depend on the number of opposing surfaces #expands (0.80)
• Room mode density rising smoothly with frequency signals good acoustics #complicates (0.75) — Eric J. Heller, Why You Hear What You Hear- An…, 2435
• Room absorption shrinks mode bandwidth and flattens standing wave peaks #complicates (0.70)