A sign, an angle, and a number of milliseconds

Inverting polarity swaps positive for negative. It is instantaneous, applies equally to 30 Hz and 15 kHz, and is exactly undone by doing it again. Two identical signals, one inverted, cancel completely at every frequency — which is what a pin 2/3 swap does to a mic that is also picked up by another, and what a reversed pair does to a loudspeaker standing next to its twin.

A phase shift is an angle at one frequency. Saying a signal is "180° out" is only the same as inverted if you also say at which frequency, because a time offset that is 180° at 500 Hz is 360° at 1 kHz and 36° at 100 Hz. The console's Ø button therefore does not shift phase; it inverts polarity, and every manufacturer who prints "phase" on it is using the word loosely. AES14 settles the convention it operates on: pin 2 is the non-inverting leg of a balanced XLR, and a positive pressure at a microphone's diaphragm gives a positive voltage there.

At the other end, a positive voltage on a loudspeaker's marked terminal should move the cone outwards, towards the listener. That is the convention IEC 60268-5 marks terminals to, and it is what "in polarity" means for a cabinet: a positive pressure in produces a positive pressure out. A 9 V battery across the terminals is still the field test, and still works.

The sum of a unit arrival and a second one at amplitude ratio r swings between 20·log(1 + r) and 20·log(1 − r). Two equal arrivals give +6 dB peaks and bottomless notches; a second arrival 10 dB down gives +2.4 and −3.3, which is a ripple of under 6 dB and not much worse than a room.

This is the quantitative reason isolation matters more than alignment. Two sources that reach a listener at the same level cannot be aligned at more than one place, and everywhere else they carve the comb above. Two sources 10 dB apart barely interact wherever they are. A coverage design that keeps the overlap zones down is worth more than any amount of delay setting, and the delay is then for the zone that remains.

Sound moves at 331.3 · √(1 + T / 273.15) metres per second, T in degrees Celsius — 343.2 m/s at 20 °C, or 2.91 ms per metre, which is the number to carry around. Humidity changes it by a few tenths of a percent and is ignored here. Temperature is the one that matters, at about 0.6 m/s per degree.

That sounds small until it is applied to a long path. A delay tower 40 m from the main array, aligned at 28 °C in the afternoon, is 2.77 ms late by the time the air has cooled to 14 °C — a first null at 181 Hz that was not there at soundcheck. Nothing has been touched; the medium has changed. Systems that read a temperature probe and retrim delays automatically exist for exactly this.

Subwoofers to mains

Two boxes covering the same frequencies from different places is the comb problem again, but at a crossover it is confined to the octave or so where both contribute — and that is where it is fixed. A sub and a main that both produce 90 Hz must arrive together at 90 Hz; a cycle there is 11.1 ms, so the tolerance is loose in absolute terms and tight in fractions of that cycle.

The polarity switch is the coarse control — it moves the sum by half a cycle at every frequency — and the delay is the fine one. The pair together can put the arrivals within a few degrees at the crossover, and a measurement system showing both phase traces overlapping through the crossover region is the evidence that they are. The alignment holds at the measurement position and along the curve where the path difference is the same; it drifts elsewhere, which is why the position is chosen to represent the audience rather than the mix.

Delay fills and towers

A fill covers listeners the main array reaches late and quietly. Its delay is the path difference from the main divided by the speed of sound — the number the calculator below gives — so that its wavefront leaves with the main's rather than ahead of it. Aligned exactly, the two sum where they overlap; and because the fill is close and the main is far, the level difference usually keeps the comb shallow, which is the previous table doing its job.

Using it: the deliberately late fill

A fill aligned exactly to the main is heard as one source somewhere between the two. Delay it a further 5 to 15 ms and the ear assigns the whole event to the main — the stage — while the fill still supplies the level and the intelligibility. The image stays where the performer is and the fill disappears as a source. That is the entire use of the effect in a PA, and it is legitimate.

What it costs is the previous section. The extra delay is a time offset, the time offset is a comb, and in the zone where fill and main are at similar levels the comb is deep. The trade is localisation against ripple in the overlap, and it is a good trade where the fill dominates its own zone and a poor one where it doesn't. The level-difference table is the tool for judging which.