Feedback howl in live sound

Why does a microphone that was perfectly quiet suddenly erupt into a screaming tone?

A microphone sits on a stand, behaving impeccably. Someone nudges the fader up a hair, or the speaker walks half a pace to the left, and within a second the room is filled with a single ferocious tone that will not stop until somebody pulls the gain down.

Two things about that are strange. The first is the suddenness — the change to the system was tiny and continuous, and the change in behaviour was neither. The second is the note. Why a pitch? Amplifying noise ought to give louder noise, not a specific frequency held with the steadiness of an organ pipe.

Start by drawing the path the sound takes. The microphone hears something, the amplifier makes it larger, the loudspeaker emits it into the room, and some fraction of that emission travels back to the microphone — which hears it again. That is a closed circuit made partly of wire and partly of air, and once you see it as a circuit, the useful question is not "how loud is the amplifier" but "what happens to a sound on one complete lap?"

Call the answer the loop gain: the factor by which a signal is multiplied on a full round trip. If a lap returns the sound at eighty percent of the amplitude it set out with, then after two laps it is at sixty-four percent, after three at fifty-one, and so on. The echoes die away in a geometric series that sums to something finite. The system is stable, and the audible symptom is mild — a faint ring, a slight hollowness, the room "hanging on" to certain notes.

Now suppose we raise the amplifier until a lap returns the sound at one hundred and five percent. Nothing about the arithmetic has changed except the base. But a number slightly below one, raised to a large power, goes to zero, while a number slightly above one goes to infinity. Take a round trip of about twenty milliseconds — roughly seven metres of air path — so fifty laps happen every second. Five percent per lap compounds to a factor of about eleven and a half over that second, which is some twenty-one decibels. In the next second it does it again. That is why nothing gradual is available to us here: below unity the sound is subtracted every lap, above unity it is multiplied, and the boundary between those two worlds is a single point that a fader can cross without visibly moving.

Why does it settle into one note rather than screaming across the spectrum? Because loop gain is not a single number — it is a number at every frequency. The microphone has response peaks, the speaker has its own, and the room contributes standing waves and reflections that make some frequencies arrive back in phase and others arrive back cancelling themselves. The sum of all that is a jagged curve, and one frequency somewhere along it is highest. As we raise the fader that frequency reaches unity first, and it alone begins compounding while everything else is still decaying. Within a fraction of a second it dominates by so many decibels that we hear nothing else. The howl is not a chosen note; it is the winner of a race that only one runner could win.

There is a second condition worth naming, since amplitude alone does not do it. The returning signal must also come back roughly in phase with itself — a whole number of cycles for the trip — or it partly cancels rather than reinforcing. Amplitude at or above unity plus phase alignment is the classical Barkhausen criterion for an oscillator, and it explains something everyone has seen: moving the microphone a few centimetres changes the path length, which changes which frequencies come back in phase, and the howl either stops or reappears at a different pitch.

And why does it not grow forever? Because the exponential is only valid while the system stays linear. Very quickly the amplifier hits its supply rails or a limiter engages, the effective gain per lap is dragged back to exactly one, and the tone parks at a steady, hideous level. What we hear is the sound of the system pinned against its own ceiling.

The practical consequences follow directly, and they are not folklore.

Getting the microphone closer to the source is the strongest move available, because it raises what the microphone hears from the singer without raising what it hears from the speaker, so the same loudness in the room needs less amplifier gain and the loop gain falls. Pointing the microphone's null at the loudspeaker does the same thing from the other side.

Opening a second microphone costs you real headroom: every open microphone contributes its own return path into the same loop, and doubling the number of open microphones costs roughly three decibels of gain before feedback. Muting what is not in use is not tidiness, it is stability.

Ringing out a room — easing the gain up until one frequency starts to sing, notching that frequency with a narrow filter, and repeating — is best understood as flattening the jagged loop-gain curve. You are not removing feedback; you are lowering the tallest peak so that the whole curve can be lifted further before any part of it reaches unity. This also explains why it has diminishing returns: each notch reveals the next peak, and eventually you are cutting so much that the sound suffers.

The misconception worth naming is that feedback is caused by "too much volume." Volume is only one term. The distance from speaker to microphone, the directional patterns of both, the room's reflectivity, and the equalisation all sit in the same product — which is why a quiet system in a tiled room can howl while a loud one on a well-arranged stage does not.

• Why in-ear monitors change this problem so completely for performers.
• What automatic feedback suppressors actually do, and what they cost in sound quality.
• How the same unity-gain reasoning appears in electronic oscillator design.

Every term the collection defines is gathered in the glossary.