11. Loudspeaker & Electroacoustics · Concept 8 of 11
Waveguide Theory
The science of shaping the horn or flare around a speaker so the sound goes exactly where you want it.
The flare walls steer the driver's wavefront into a defined coverage angle, with the cone edges set at the -6 dB half-pressure points.
What it is
Shaping a horn or flare around a driver so the sound is steered into a defined coverage angle instead of spraying everywhere.
Key facts
Speed of sound in air = 343 m/s at 20 degrees C (rises about 0.6 m/s per +1 degree C)
Wavelength: lambda = c / f, where lambda = wavelength (m), c = speed of sound (343 m/s), f = frequency (Hz). So 1 kHz = 0.34 m, 100 Hz = 3.4 m, 10 kHz = 34 mm
A horn only controls its pattern down to where its mouth width is roughly >= one wavelength; below that it loses grip
Coverage is quoted H x V in degrees: e.g. 90x40, 60x40, 90x60, 120x60, 100x100 (horizontal x vertical)
The pattern edge is the -6 dB point: half the on-axis sound pressure (a quarter of the power)
-3 dB = half the POWER (0.707 of pressure); -6 dB = half the PRESSURE
Point source: doubling distance = -6 dB SPL (inverse-square). Line array near field: only about -3 dB per doubling
Mouth size controls LOW frequencies; throat/flare rate controls HIGH frequencies
Constant-directivity (CD) horns hold their angle across frequency but roll off highs ~6 dB/octave, needing HF EQ boost
Coverage rule: aim adjacent boxes so their -6 dB edges meet for even, hotspot-free summed coverage
How it works
Sound leaves the tiny driver throat as a near-point source wanting to spread in all directions.
The curved flare walls progressively guide and load the wavefront outward.
Wall angle and flare rate set the exit spread (e.g. 90 degrees wide, 40 degrees tall).
Mouth size must be at least one wavelength wide to control that frequency's spread.
Below the control frequency the pattern widens and the horn loses grip (more spill).
Result: a defined cone of even coverage, edges set by the -6 dB down points.
Real examples
A 90x40 PA top over a dance floor: 90 deg wide covers the crowd, 40 deg tall stops energy hitting the ceiling and rear wall.
Two tops splayed so each one's -6 dB edge overlaps the other = seamless, hotspot-free coverage front to back.
Narrow 60x40 long-throw box aimed down a deep room to reach the back rows without blasting the front.
CD horn measured flat on-axis but dull until an HF shelf EQ restores the top end (the ~6 dB/oct CD roll-off).
Cheap conical horn that beams (narrows) at high frequencies, so people off to the side lose all the sparkle.
How it helps in live sound
Pick coverage by room shape: wide crowd = 90/100 deg horizontal; long deep room = 60 deg for throw.
Aim the -6 dB edges of neighbouring boxes to MEET, not overlap heavily (overlap = comb-filter smear and hot middle).
Point the vertical pattern so its top edge clears the back wall and ceiling to cut slap-back reflections.
On CD horns add a high-shelf boost (roughly +3 to +6 dB above 3-4 kHz) to fix the natural HF roll-off.
Use the spec sheet H x V numbers plus a laser/angle to map who is on-axis vs in the dead zone, not guesswork.
Low frequencies are nearly omni (mouth too small to steer them), so control bass with sub placement/cardioid arrays, not the horn.
Everyday analogy
Cupping your hands around your mouth funnels your shout at one mate across the room instead of letting it scatter to everyone.
Watch out
Myth: a 90 degree horn is loud and even right out to 45 degrees off-axis. Truth: the edge is the -6 dB point (half pressure), so it is already noticeably quieter there, and the rated angle only holds above the horn's control frequency.
Fun fact
A horn does double duty: it not only aims the sound, it acoustically matches the tiny driver to the big air load like a gearbox, lifting efficiency from a few percent toward 20-50 percent.
Key takeaways
The flare shape decides exactly how wide and how tall the sound goes.
Coverage edges are the -6 dB (half-pressure) points, quoted as H x V degrees.