A sound off to one side hits the near ear a tiny bit before the far ear, and your brain uses that gap to find direction.
A source on the left reaches the near ear first; the ~0.6 ms gap to the far ear is the ITD your brain decodes into direction.
What it is
A sound off to one side reaches your near ear slightly before your far ear, and your brain reads that tiny gap to pin down direction.
Key facts
Speed of sound in air = 343 m/s at 20 degrees C (rises ~0.6 m/s per +1 degree C)
1 ms of delay = ~0.34 m of extra sound path (343 m/s x 0.001 s)
Max human ITD ~0.6 to 0.7 ms (~660 microseconds) for a source at a full 90 degrees to one side
Interaural distance (ear to ear) ~17 to 18 cm; acoustic path round the head to the far ear ~0.21 to 0.23 m
Woodworth formula: ITD = (r / c) x (theta + sin theta), r = head radius (m), c = 343 m/s, theta = angle off-centre (radians)
ITD is the DOMINANT direction cue BELOW ~1500 Hz; above that, ILD (level difference) takes over (duplex theory)
1500 Hz wavelength ~0.23 m ~= one head-width, where phase wraps and ITD turns ambiguous
Minimum Audible Angle ~1 degree straight ahead, equal to detecting ITD shifts of only ~10 microseconds
Brain uses phase delay at low freq and onset/envelope timing at higher freq to read the gap
Precedence (Haas) effect: the FIRST arrival sets perceived direction for delays of ~1 to 35 ms even if the later sound is louder
How it works
Sound source sits off to one side, not dead centre.
Wavefront reaches the near ear first because it is physically closer.
It then travels the extra path around the head to reach the far ear.
Extra distance divided by 343 m/s gives the time gap (the ITD).
Brain compares the two ear signals and maps the delay to an angle.
Bigger delay = further to the side; zero delay = straight ahead or behind.
Real examples
Friend taps your left shoulder: left ear hears it ~0.5 ms before the right, brain says 'left'.
A car passing on your right: ITD swings from negative to zero to positive as it crosses in front.
Plug one ear and bass-heavy sound becomes very hard to locate.
Headphones delaying one channel by 0.3 ms shifts a mono voice off-centre with no level change.
Sub bass at 50 Hz is easy to localise from steady phase: the wavelength is huge compared with the head, so the timing/phase cue is clear and unambiguous (phase only gets ambiguous at high frequencies).
How it helps in live sound
Time-align L/R mains and delay stacks: even 1 to 2 ms mismatch smears the stereo image.
Remember 1 ms ~= 0.34 m: measure speaker-to-listener distances and dial delay in ms so arrivals line up.
Use Haas: delay-fills should arrive 10 to 25 ms AFTER the mains so sound still images to the stage, not the fill.
Watch sub vs top timing: out-of-step subs cause low-mid comb filtering and vague low-end position.
For mono PA, ITD is moot; for stereo/LCR, measure with a dual-channel analyser (Smaart) and trim delay in ms, not guesswork.
Avoid huge L/R spacing: it widens the image but blurs the centre vocal.
Everyday analogy
It is like two race timers at a finish line: the runner trips the near beam a fraction of a second before the far one, and that split tells you which lane they were in.
Watch out
Myth: ITD works at all frequencies. Truth: above ~1500 Hz the wavelength is shorter than the head so phase wraps and becomes ambiguous, and the brain switches to level difference (ILD) instead.
Fun fact
Your brain can resolve an interaural delay of about 10 microseconds, and that alone is enough to hear a 1-degree shift in a sound straight ahead of you.