Hard-walled rooms behave as three-dimensional resonators with many audible modal frequencies

Evidence

While Figures 2.19 and 2.21 characterize the temporal evolution of a sound field in a room, another picture is obtained by looking at sound transfer properties in the frequency domain. A hard-walled room can be understood as a three-dimensional resonator where a large number of modal frequencies can be found in the audible frequency range. For a rectangular room with hard walls, the frequencies of normal modes can be computed analytically from where c is the sound velocity; Lx, Ly, and Lz are the dimensions of the room in the three directions; and integer variables nx, ny, and nz are given all the combinations of the values 0, 1, 2, . — Ville Pulkki, Matti Karjalainen, Communication Acoustics- An…, 291

Categorization

• corroborated: 3 independent passages support this claim — Ville Pulkki, Matti Karjalainen, Communication Acoustics- An…, 291
• XREF: connects to: Perfectly hard-walled halls would produce unbearably long echoes needing leaks to tame; Churches embedded damped Helmholtz resonators in their walls for centuries to absorb sound — Eric J. Heller, Why You Hear What You Hear- An…, 1269; Instrument bodies act as coupled resonators that shape and radiate sound (+14 more)

Broader Connections

• Spatially proportional room dimensions create coincident resonant modes #expands (0.85)
• Spatially static resonant modes cause sound level to vary across a room #expands (0.80) — David M. Howard, Jamie Angus, Acoustics and Psychoacoustics, 1953
• Avoiding commensurate room dimensions prevents overlapping modal frequencies that cause acoustic problems #corroborates (0.80)
• Rectangular rooms allow predicting low-frequency modal behavior in advance #corroborates (0.80) — Toole, Floyd E, Sound reproduction- the acoustics and…, 1635
• Modal decay analysis governs room acoustics below the critical frequency #corroborates (0.80) — David M. Howard, Jamie Angus, Acoustics and Psychoacoustics, 2038
• Room modes are determined by the linear dimensions of opposing surfaces #expands (0.80)
• A transition frequency separates modal from ray acoustical behavior in rooms #expands (0.78) — Toole, Floyd E, Sound reproduction- the acoustics and…, 475
• Room echoes sculpt sharp resonant peaks into a sound’s spectrum #expands (0.78)
• Room modal frequencies depend on the number of opposing surfaces #expands (0.75)
• Steady-state frequency response is the reliable indicator of audible room resonances #corroborates (0.75) — Toole, Floyd E, Sound reproduction- the acoustics and…, 956
• Resonances near anechoic thresholds become audible again in reflective rooms #expands (0.75) — , Toole, Floyd E - Sound reproduction-…, 399
• Room mode density rising smoothly with frequency signals good acoustics #expands (0.72) — Eric J. Heller, Why You Hear What You Hear- An…, 2435