Directivity Index

Same watts, two speakers: low DI sprays a sphere of sound, high DI focuses a beam onto the crowd.

What it is

A single decibel number rating how tightly a speaker focuses sound forward versus spraying it everywhere.

Key facts

• DI = 10 x log10(Q), where Q is the Directivity Factor (a pure ratio) and DI is in dB.
• Q = on-axis intensity divided by the intensity of an equal-power omni source at the same distance.
• Omni point source: Q = 1, DI = 0 dB. Each doubling of Q adds +3 dB to DI.
• Q = 2 = +3 dB; Q = 4 = +6 dB; Q = 8 = +9 dB; Q = 10 = +10 dB.
• Boundary loading is free DI: half-space (wall) Q2 +3 dB, quarter-space (corner) Q4 +6 dB, eighth-space Q8 +9 dB.
• Typical horn-loaded PA tops run Q = 10 to 30, i.e. DI = +10 to +15 dB on-axis.
• DI is frequency-dependent: low frequencies stay near omni, high frequencies beam, so DI rises with pitch.
• Rough rule: Q approx 25000 / (H x V), with H and V the -6 dB coverage angles in degrees.
• Speed of sound = 343 m/s in air at 20 C; 10 kHz wavelength is 3.43 cm, so HF beams hardest.
• Doubling acoustic power = +3 dB; perceived 'twice as loud' needs about +10 dB. Higher DI = more on-axis dB per watt.

How it works

1. Drive speaker with a known power; measure sound intensity on-axis at fixed distance.
2. Average the intensity over a full sphere around the speaker (the total power spread everywhere).
3. Q = on-axis intensity divided by that spherical-average intensity.
4. DI = 10 x log10(Q): convert the ratio into decibels.
5. Higher Q/DI = energy crammed into a narrow beam; lower = spread wide and even.

Real examples

• Omni mic/point source: Q = 1, DI = 0 dB, sound goes everywhere equally.
• PA top in a 90 x 60 horn: roughly DI +9 to +11 dB, beam aimed at the crowd.
• Subwoofer at 50 Hz: nearly omni, DI near 0 dB, which is why bass leaks behind the stage.
• Line array: stacks boxes to raise vertical DI, throwing level to the back rows, not the ceiling.
• A speaker tucked into a wall corner gains DI for free from boundary loading (Q jumps to 4 or 8).

How it helps in live sound

• Pick boxes by DI/coverage: a 90 x 40 horn over 60 x 40 puts more dB on the audience, less on walls = less feedback.
• Aim high-DI tops at ear height of the back of the crowd, not the empty ceiling, to claw back gain-before-feedback.
• Subs are low-DI (near omni): place them where rear spill won't matter, or build a cardioid sub array.
• Higher DI = more direct-to-reverberant ratio = clearer speech in boomy rooms (halls, gyms, churches).
• Read the spec sheet: look for the DI/Q vs frequency plot, not just the nominal coverage angle.
• Tight HF beaming means a step off-axis can drop you -6 dB or more, so cover the whole crowd, don't over-narrow.