It is the rule that sound gets dramatically quieter the further you move away from the source.
Each doubling of distance spreads the same sound over 4x the area, dropping the level a fixed 6 dB.
What it is
The rule that sound level drops 6 dB every time you double your distance from the source, because the same energy spreads over a bigger area.
Key facts
Inverse square law: sound INTENSITY (power per area) drops with the SQUARE of distance. Double distance = 1/4 the intensity.
Level drop = -6 dB SPL per distance doubling (a clearly audible drop, though not 'half as loud' to the ear, which needs about 10 dB).
Formula: dB change = 20 x log10(d1 / d2). d1 = old distance, d2 = new distance, both in metres.
Intensity formula: I = P / (4 x pi x r^2). I = intensity (W/m^2), P = source power (watts), r = radius/distance (m), 4 x pi x r^2 = surface area of a sphere.
10x the distance = -20 dB. 100x the distance = -40 dB.
Speed of sound in air = 343 m/s at 20 C (about 1235 km/h). It rises ~0.6 m/s per +1 C.
0 dB SPL = threshold of hearing (20 micropascals). 120 dB SPL = pain threshold.
+10 dB is perceived as roughly 'twice as loud' to the ear; +6 dB is double the SOUND PRESSURE, not double loudness.
Energy is NOT lost in the law itself: it spreads thinner over a 4x bigger sphere each doubling. Real-world extra loss comes from air absorption (worse at high freq) and obstacles.
Reference distance for spec sheets: speaker SPL is quoted at 1 m (e.g. '129 dB SPL @ 1m'). Predict any distance from there.
How it works
Find the speaker's rated SPL at 1 m from the spec sheet.
Note your listener distance in metres.
Plug into dB change = 20 x log10(1 / distance).
Subtract that from the 1 m SPL to get level at the listener.
Each time you double distance again, just take off another 6 dB.
Add separate losses for air absorption and obstacles on top.
Real examples
129 dB @ 1 m becomes 123 dB @ 2 m, 117 dB @ 4 m, 111 dB @ 8 m.
Front row at 2 m vs back at 32 m: that is 4 doublings = 24 dB quieter, why the back feels gutless.
Move a mic from 5 cm to 10 cm off a guitar amp and the signal drops 6 dB.
A 100 W point source at 1 m gives ~8 W/m^2; at 2 m only ~2 W/m^2 (a quarter).
How it helps in live sound
Use delay speakers ~20-40 m back, time-aligned, to top up the -24 dB hole at the rear without blasting the front.
Quote and design from the '@1m' SPL spec, then subtract 6 dB per doubling to the furthest punter.
Close-mic for max gain-before-feedback: halving mic distance buys +6 dB of clean level.
Fly mains higher and aim down so front-to-back distance ratio shrinks, flattening the 6 dB-per-double drop.
Cardioid/end-fire sub arrays cut spill backstage, but remember subs still obey the inverse square law for level.
In a room, only the direct field follows the law cleanly; past the critical distance reverberation dominates.
Everyday analogy
Like spray paint from a can: a tight dense dot up close, but the same paint smears thin and faint as you step back, because it covers a much bigger patch.
Watch out
Myth: 'double the distance, half the volume.' Wrong: doubling distance loses 6 dB (a quarter of the intensity), and the ear needs about 10 dB to perceive 'half as loud'.
Fun fact
The law is purely geometric: it works the same for light, gravity and radio waves, because anything radiating from a point spreads over a sphere whose area grows with r-squared.
Key takeaways
Double the distance = -6 dB, every single time.
Intensity falls with distance SQUARED (1/4 at 2x, 1/9 at 3x).
Energy isn't destroyed, just smeared over a bigger sphere.
This is exactly why front rows deafen and back rows starve.
Delay speakers and good aim exist to beat this drop-off.