Sound in a Room

A room is a set of surfaces that hand your sound back to you, late and altered, hundreds of times over. Everything difficult about working indoors follows from that one fact. It is the exact inverse of the free field: outdoors the wave leaves and never returns, and indoors an ear gets the sound you sent plus every delayed copy the walls have made of it.

Musicians treat the room as a flavour laid over the mix, something a graphic EQ ought to subtract. It cannot. The room decides which bass notes are loud and where you have to stand to hear them, how long each note hangs on after the player stops, and how much of your gain does anyone any good. The building's dimensions and surfaces settle most of that before you unload the van.

Every Boundary Is a Second Source

When a wave meets a wall, some energy bounces back, some turns to heat inside the material, and some passes on to the neighbours. The bounced share behaves like a mirror image: a listener gets the real source plus a copy sitting the same distance behind the surface. Put a source much closer to a boundary than one wavelength and that image lands effectively on top of it. Two coherent sources in one place double the pressure, and doubled pressure is 6 dB. Half of that is radiation squeezed into half the space; the other half is the boundary loading the driver harder, so it puts out twice the power for the same cone travel. A floor plus a wall gives up to 12 dB, a corner up to 18.

You will also see "+3 dB per surface" quoted, and it is not wrong — it answers a different question. Hold radiated power fixed, halve the solid angle it goes into, and intensity doubles for 3 dB, six at a wall-floor junction and nine in a corner. That is the figure once the reflection stops arriving in step. Six decibels per boundary is a low-frequency ceiling, not a promise.

The reflection that adds at long wavelengths subtracts at short ones. When the round trip to a surface and back equals half a wavelength, the returning copy is inverted and cancels — at f = 343 ÷ (4 × d), with d the source-to-surface distance in metres. A cabinet a metre off the back wall has a null near 86Hz; half a metre moves it to about 172Hz. A kick drum in a corner is louder underneath and notched above, which is what "boomy and gutless at once" actually is.

Small Rooms Have Favourite Bass Notes

A room resonates when one of its dimensions holds a whole number of half wavelengths: the reflection returns in step with the wave that made it, and the two settle into a stationary pattern of loud and quiet zones. Divide the speed of sound by twice the dimension for the lowest frequency, then multiply by whole numbers for the rest — f = n × 343 ÷ (2L). These are the axial modes, the strongest of the set and the ones worth working out by hand.

The 8.6 m of a 40Hz wave from the first lesson is what gives that formula teeth, because half of 8.6 m is 4.3 m and any dimension near 4.3 m resonates at 40Hz. Take a club room 11 m long, 7 m wide and 3.5 m high, about 36 by 23 by 11.5 ft. The length gives 15.6, 31.2, 46.8, 62.4 and 78Hz. The width gives 24.5, 49 and 73.5. The height is exactly half the width, so it gives 49 and 98 and stacks straight onto two of the width's modes. Three modes crowd between 46.8 and 49Hz, and three more — 62.4, 73.5 and 78 — sit inside the 50 to 80Hz band a kick drum lives in.

Modes only rule the bottom. Above the Schroeder frequency, 2000 × √(RT60 ÷ V) with RT60 the decay in seconds and volume in cubic metres, they overlap too thickly to pick out one at a time. Empty, this room crosses over near 133Hz; pack it with bodies and the shorter decay drags that down to roughly 77Hz, so a full house is modal over a narrower band than an empty one. Underneath the crossover, where you stand changes the note. Above it, position still matters, but never that violently.

Reverb Time Decides Whether the Words Survive

Reverberation is the tail. A player stops, and the room goes on returning what it already took in, quieter each time round, until there is nothing left to return. RT60 puts a number on that: the interval over which the tail sheds 60 dB, which is a millionth of the power it began with. Sabine's formula estimates it as RT60 = 0.161 × V ÷ A, with V the volume in cubic metres and A the total absorption in square-metre sabins, every surface counted at its own absorption coefficient. In feet the constant is 0.049.

Sabine holds while a room is fairly live, average absorption coefficient under about 0.2. Past that it overstates the decay, and taken to the limit it predicts a reverb time for a room that absorbs everything, which is impossible. Use Norris–Eyring in absorptive rooms: RT60 = 0.161 × V ÷ (−S × ln(1 − ā)), S being total surface area and ā the average coefficient. Empty, with hard surfaces averaging around 0.13, that club room decays in about 1.2 seconds and the two formulas land about seven percent apart. Add 120 people, each worth roughly 0.45 m² of absorption, and the average climbs past 0.3: Sabine says 0.48 seconds, Eyring says 0.40.

Long decay is what makes a hall feel generous, short decay is what lets speech survive, and you cannot have both. A symphony hall is built to 1.8 to 2.2 seconds, a stone church runs 3 to 8, and classroom standards hold a small room to 0.6. Speech-critical rooms are designed for 0.4 to 0.8, because consonants are brief and quiet and a long tail buries them under the vowel before. Play a hard church hall and you get both halves at once: enormous chords, and nobody able to make out the verse.

Direct Sound, Reverberant Sound, and Where One Takes Over

What arrives at a listener indoors splits into two parts that behave nothing alike. The direct sound is the first arrival, straight from the box, and distance treats it exactly as an open field would: 6 dB gone per doubling. Everything behind it is the reverberant field, which is near enough one constant level filling the whole space.

Add them and the curve of level against distance bends. Near the source the direct part dominates and level falls off as it would in an open field. Further out the reverberant part takes over and the curve flattens, so the back wall is barely quieter than halfway back. That is why a club PA can be a fraction of an outdoor rig and still feel as loud: the previous lesson said a room props the level up at the back, and this is the mechanism.

It is not free. What props the level up is a time-smeared copy of the music, so the further out somebody stands the more of what they hear is room rather than band. Indoors, level and clarity stop being the same quantity.

Critical Distance Caps How Much Gain Is Worth Having

Critical distance is where the two fields are equal in level. Inside it an audience is mostly hearing you; outside it they are mostly hearing the room. Two quantities set it. The first is the directivity factor of the box, written Q — how much intensity it lands on axis compared with an omnidirectional source radiating the same total power. An omni box is Q = 1, and every degree of focus raises it. Two coverage angles give you an estimate, Q = 180 ÷ arcsin(sin(θ ÷ 2) × sin(φ ÷ 2)), which puts a 90 by 60 degree box near 8.7. The second is the room constant, R = S × ā ÷ (1 − ā). Then Dc = 0.141 × √(Q × R), and that constant works in metres or in feet so long as you stay consistent. From a measured decay instead, Dc = 0.057 × √(Q × V ÷ RT60) gets you there in metres.

Run that club room empty and R comes out near 42 m². An omnidirectional source has a critical distance of 0.9 m, which is arm's length. That 90 by 60 box stretches it to 2.7 m; fill the room with those 120 people and it reaches about 4.8 m. In a hard room nearly the whole audience stands beyond critical distance, and that caps your gain. Turn the system up and both fields rise together, because one box feeds both, so the ratio of band to room at a given seat is set by geometry and absorption. The master fader appears nowhere in it.

Past critical distance, more level buys loudness and nothing else. Step out to double that distance and the room's share quadruples, because the direct component has dropped another 6 dB and the reverberant field has not moved at all. The same arithmetic sets your feedback ceiling. Outdoors, doubling the speaker-to-microphone distance buys 6 dB every time; indoors it buys that only until the microphone passes critical distance, after which it sits in a field of constant level and moving it further achieves nothing. The moves that still work are the ones that shrink the room's share: tighter coverage, boxes aimed into bodies rather than at plaster, and absorption wherever you can get it.

Reading a Room Before Load-In

• Clap once from the middle of the empty floor and listen to what follows — a fast metallic ring is flutter echo between parallel hard walls; a long smooth tail is a live room; nothing at all behind the clap is a dead one that will want more power than its size suggests.
• Pace the two long dimensions — 343 divided by twice each dimension in metres gives the lowest mode, and its multiples give the rest. Anything between 50 and 80Hz will argue with your kick.
• Walk the floor while somebody sustains a low note — the loud and quiet spots are a map you can draw in thirty seconds. The desk belongs in neither.
• Keep subs out of the corner unless you want the corner's answer — three surfaces can hand you 18 dB, but only at the very bottom, with a cancellation notch above it.
• Measure from each cabinet to the wall behind it — 343 divided by four times that distance is where the notch sits, and the fix is to move the box closer to the wall rather than further off it. Tightening up to 30 cm pushes the notch past 280Hz; backing away to 1.2 m walks it down to 71Hz, straight into the band you were protecting.
• Assume the room shortens when it fills — a full house can halve the reverb time and push critical distance out with it, so an empty-room soundcheck is a worst case, not a preview.
• Aim before you reach for EQ — coverage kept off a wall never joins the reverberant field, while EQ scales both fields together and cannot improve that ratio at all.