A simple PA (public address) system consists of a microphone, an amplifier and one or more speakers. Whenever you have those three components, you have the potential for feedback. Feedback occurs when the sound from the speakers makes it back into the microphone and is re-amplified and sent through the speakers again.
Imagine, for example, that you place the microphone in front of the speaker. Now you tap on the microphone. The sound of the tap goes through the amplifier, comes out the speaker, re-enters the microphone, etc. This loop happens so quickly that it creates its own frequency, which we hear as a howling sound. The distance between the mike and the speakers has a lot to do with the frequency of the howling, because that distance controls how quickly the sound can loop through the system.
You can actually try this out on your computer if your computer has speakers and a microphone. In Windows, you need to enable the microphone and speakers using the volume control (which you can access by double clicking on the speaker icon in the system tray).
Make sure that in this dialog the microphone and speakers are not muted and are at maximum volume (if the microphone control is not visible, select it in Properties). If you have it set up right, you should be able to tap the microphone and hear it in the speakers. Now place the microphone near the speakers and turn up the speaker volume until you hear the feedback. Try changing the distance between the mike and speakers and see what effect that has on things.
If you are setting up a sound system and want to avoid feedback, there are a few general rules that can help you avoid the problem:
1) Make sure the speakers are in front of the microphone and pointing away from the microphone. If the speakers are behind the microphone, then feedback is nearly guaranteed.
2) Use a unidirectional microphone.
3) Place the microphone close to the person who is speaking/performing.
4) If you have access to an equalizer, dampen the frequencies where feedback is occurring.
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