Audio Feedback
Audio feedback occurs when a sound loop exists between an audio input (for example, a microphone or guitar pickup) and an audio output (for example, a loudspeaker). In this example, a signal received by the microphone is amplified and passed out of the loudspeaker. The sound from the loudspeaker can then be received by the microphone again, amplified further, and then passed out through the loudspeaker again. This is a good example of positive feedback. The frequency of the resulting sound is determined by resonant frequencies in the microphone, amplifier, and loudspeaker, the acoustics of the room, the directional pick-up and emission patterns of the microphone and loudspeaker, and the distance between them.
More specifically, the conditions for feedback follow the Barkhausen criterion, namely that an oscillation occurs in a feedback loop whose delay is an integer multiple of 360 degrees and the gain is equal to or greater than 1 (both at the given feedback frequency). If the gain is greater than 1, then the system can start to oscillate out of noise, that is to say: sound without anyone actually playing. If the gain is large, but less than 1 then the high pitched feedback tones will only be created with some input sound and will slowly decay.
Prevention
Most audio feedback results in a high-pitched squealing noise familiar to those who have listened to bands at house parties, and other locations where the sound setup is less than ideal - this usually occurs when live microphones are placed in the general direction of the output speakers. Professional setups circumvent feedback by placing the main speakers a far distance from the band or artist, and then having several smaller speakers known as monitors pointing back at each band member, but in the opposite direction of the microphones.
Feedback can be reduced manually by "ringing out" a microphone. The sound engineer can increase the level of a microphone or guitar pickup until feedback occurs. The engineer can then turn down frequency on a band equalizer preventing feedback at that pitch but allowing maximum volume. Professional sound engineers can "ring out" microphones and pick-ups by ear but most use a real time analyzer connected to a microphone to show the ringing frequency.
To avoid feedback, automatic anti-feedback devices can be used. (In the marketplace these go by the name "feedback destroyer" or "feedback eliminator".) Some of these work by shifting the frequency slightly, resulting in a "chirp" -sound instead of a howling sound due to the up shifting the frequency of the feedback. Other devices use sharp notch-filters to filter out offending frequencies. Adaptive filters can be used to tune these notch filters.