Diffuse Field Theory

The idea that in a lively room, sound bounces around so much it ends up roughly equal and random everywhere.

Direct sound stays clean only inside the Critical Distance; past it the random diffuse wash buries it.

What it is

In a live room, sound bounces so many times it becomes a random, even wash of energy arriving from all directions at once.

Key facts

Speed of sound in air = 343 m/s at 20 degC (rises ~0.6 m/s per +1 degC); sound covers ~1 m in ~2.9 ms
Diffuse field = sound energy density equal everywhere + arriving from all angles equally with random phase
+6 dB = double the sound PRESSURE; +10 dB = perceived 'twice as loud'; -3 dB = half POWER; -6 dB = half pressure
Inverse-square law: direct sound drops 6 dB per DOUBLING of distance; the diffuse field stays roughly FLAT with distance
Critical Distance (Dc) = where direct level = reverberant level; past Dc the room wins
Dc = 0.057 x sqrt(Q x V / RT60): Q=speaker directivity, V=room volume m3, RT60=reverb time s
RT60 = time for sound to decay 60 dB after the source stops (the standard reverb measure)
Sabine: RT60 = 0.161 x V / A, where V=volume m3 and A=total absorption in sabins (sum of area x absorption coeff)
Absorption coefficient runs 0 (perfect reflector, e.g. concrete) to 1.0 (open window / total absorber)
Speech wants RT60 ~0.6-1.0 s; over ~1.5 s words smear; cathedrals hit 6-10 s

How it works

Source fires; first arrival is the DIRECT sound (clean, one direction).
Walls/ceiling/floor reflect it; each bounce loses energy to absorption.
After many bounces, reflections come from all angles with random timing and phase.
Energy density evens out across the room, the diffuse (reverberant) field.
Direct level falls with distance; diffuse level stays flat, so they cross at Critical Distance.
Past Critical Distance the wash dominates and clarity collapses.

Real examples

School gym / hall: bare concrete + steel, RT60 2-3 s, vocals turn to mush past a few metres.
Marquee with hard floor + tarp walls: reflective, washy, hard to keep speech crisp.
Church/cathedral: RT60 6-10 s, lovely for organ, terrible for a compere.
Carpeted function room with drapes + bodies: RT60 ~0.5 s, near-dead, easy to mix.
Outdoor gig: almost no reflections, pure direct field, inverse-square rules, levels drop fast with distance.

How it helps in live sound

Work INSIDE Critical Distance: get tops/fills closer to people so direct beats the wash.
Use higher-directivity boxes (bigger Q) to push Dc further back and throw clean sound.
Aim and tilt cabinets AT the audience, not at hard walls/ceiling, fewer reflections feeding the field.
Cut low-mids (200-500 Hz) to drop RT60-fuelled mush; high-pass vocals around 100-120 Hz.
Add 'absorption' for free: bodies, drapes, carpet; a packed room is way drier than an empty soundcheck.
Ride levels tighter and use delays/fills so you don't crank the mains and just pump more energy into the reverb.

Everyday analogy

Spray perfume in a room and wait a minute: the smell is roughly the same wherever you stand, just like reverberant sound spreads out evenly after enough bounces.

Watch out

Myth: 'turn it up and they'll hear it better.' Past Critical Distance more volume just feeds the reverberant wash equally, so intelligibility gets WORSE; move the box closer or tighten directivity instead.

Fun fact

Inside the diffuse field, level barely changes as you walk around, so a stadium's far corner can read nearly the same SPL as mid-floor even though the direct PA sound is long gone.

Key takeaways

Diffuse field = even, random sound from every direction after many bounces.
Direct sound drops 6 dB per distance doubling; the diffuse wash stays flat.
Critical Distance is where direct = reverberant; beyond it the room wins.
Lively/washy rooms bury your direct sound and kill clarity.
Fix it physically: closer boxes, tighter aim, more directivity, more absorption.
RT60 over ~1.5 s smears speech; turning up just feeds the reverb.