Perfectly hard-walled halls would produce unbearably long echoes needing leaks to tame

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 (#expands, via linked claim)

Categorization

• XREF: connects to: Walls must be rough on many scales to scatter sound diffusely; Hard-walled rooms behave as three-dimensional resonators with many audible modal frequencies — Ville Pulkki, Matti Karjalainen, Communication Acoustics- An…, 291

Related

• Hard-walled rooms behave as three-dimensional resonators with many audible modal frequencies (similarity 0.89)
• Every room has a low-frequency limit below which modal effects dominate (similarity 0.83)
• Room mode density rising smoothly with frequency signals good acoustics (similarity 0.82)
• Room modes are determined by the linear dimensions of opposing surfaces (similarity 0.81)
• Spatially static resonant modes cause sound level to vary across a room (similarity 0.81)
• Axial mode frequencies are computable from room dimensions by a simple formula (similarity 0.81)
• Spatially proportional room dimensions create coincident resonant modes (similarity 0.81)
• Walls must be rough on many scales to scatter sound diffusely (similarity 0.80)
• Reflections from a nearby hard wall can double the sound amplitude toward the listener (similarity 0.80)
• Room acoustics requires modeling direct sound then early reflections (similarity 0.80)
• Rectangular rooms allow predicting low-frequency modal behavior in advance (similarity 0.79)
• For short wavelengths, walls only confine sound rather than amplify its power. (similarity 0.79)
• Room acoustical behavior changes across a broad transition region, not at one frequency (similarity 0.79)
• Room boundary reflections are the second loudest sounds a listener hears (similarity 0.79)
• Low-frequency room response depends on woofer distances to floor and walls (similarity 0.79)

Broader Connections

• Hard-walled rooms behave as three-dimensional resonators with many audible modal frequencies #expands (0.82) — Ville Pulkki, Matti Karjalainen, Communication Acoustics- An…, 291
• Walls must be rough on many scales to scatter sound diffusely #complicates (0.78)