There is a frequency, different for every room, below which everything you know about room acoustics stops applying. Above it a room is statistical: so many modes overlap at once that they merge into a continuous diffuse field, reverberation time means something, and where you stand hardly matters. Below it a room is modal: a handful of separated resonances, each with its own pattern of loud and quiet places, and the response depends enormously on where the source is and where the listener is.
The dividing line is the Schroeder frequency, f = 2000 · sqrt(RT/V) in metric units. For a 17,000 m³ concert hall at 2 s it is about 22 Hz — below anything an orchestra produces, which is why hall design can treat the room as statistical throughout and why the textbook rules work there. For a 60 m³ control room at 0.3 s it is about 141 Hz. That is not an obscure corner of the spectrum. It is the bottom two octaves of nearly all recorded music, the region every mix decision about bass is made in, and in a small room it is governed by rules that have nothing to do with absorption coefficients.
What lives down there
Between rigid parallel surfaces, sound sets up standing waves at frequencies where the room dimension is a whole number of half wavelengths. In a rectangular room the general expression is
f = (c/2) · sqrt( (nx/Lx)² + (ny/Ly)² + (nz/Lz)² )
with nx, ny, nz any non-negative integers not all zero. Where one index is non-zero the mode is axial and runs between one opposed pair of surfaces; those carry the most energy and are the ones heard as a boom. Two non-zero indices give a tangential mode, four surfaces, roughly half the energy. Three gives an oblique mode, all six surfaces, weaker again.
The modes are not a defect. Every room has them and always will. The defect is their distribution. If a room’s dimensions share a common factor — the 3 m by 3 m by 3 m cube being the pathological case, but 6 m by 3 m by 2.4 m is nearly as bad — then many modes pile onto the same frequency and leave gaps either side. The ear reads a pile-up as a boom at that note and a gap as a hole, and the effect is that a bass line played up a scale is uneven from note to note. That unevenness is the single most common complaint about small rooms, and it is decided entirely by three numbers on the plan.
Why absorption will not save you
The instinctive fix is to add bass absorption. It helps, and it is not sufficient, for two reasons that are worth separating.
The first is depth. A porous absorber works where the air particle velocity is high, which is a quarter wavelength away from a boundary. At 60 Hz a quarter wavelength is 1.43 m. To absorb a 60 Hz mode with mineral wool you need roughly a metre and a half of depth, or a tuned resonant device occupying a good fraction of that, and in a room 2.4 m high there is nowhere to put it. This is why the shallow foam sold as bass trapping does essentially nothing below 200 Hz.
The second is placement, and it is the more interesting one. A mode has a pressure maximum at every boundary and a pressure minimum somewhere in the middle. A pressure-based absorber has to be at a maximum to do any work, and a velocity-based one at a minimum. Put the wrong type in the wrong place and it is furniture. Corners are the only locations that are a pressure maximum for every mode at once, which is why corner traps are the standard advice, and also why the standard advice runs out as soon as the corners are full.
Even done perfectly, absorption lowers and broadens the peaks. It does not move them. A room whose modes are bunched at 46 Hz stays bunched at 46 Hz; it simply becomes a less pronounced bunch. The distribution is geometry, and geometry is not a material property.
Which is why we ask for the section early
The ratios that spread modes evenly have been tabulated since Bolt in the 1940s, and there is no single right answer — 1 : 1.4 : 1.9 and 1 : 1.6 : 2.33 are two of the good ones, and any set with no small common factors will do most of the job. What matters is that the choice is free at concept stage and unaffordable afterwards. Moving a wall 400 mm on a drawing costs an afternoon. Moving it once the slab is poured costs more than the entire acoustic budget of the project.
So when we are asked to review a small critical room and the plan is already fixed, our first question is whether it is genuinely fixed, and our second is what the ceiling can do — because a non-parallel or stepped ceiling is often the last dimension still negotiable and can break up the vertical axial series on its own. And when we are brought in at the right moment, the proportions cost nothing at all. They are the cheapest acoustic treatment that exists, and the only one that works at 40 Hz.
