# The Limitation of Feedback

If you speak one word at the microphone at a level of 80 dB and the loudspeaker returns that word to the microphone at 80 dB, then you can go home. The sound system will repeat the sound all day, "chasing its tail" from microphone to loudspeaker.

The situation depicted here is the theoretical maximum gain where the feedback signal is equal to the input signal. It is not practical to get this kind of gain, so you seek to stay considerably below this - at least 3dB is a common rule. Any time the feedback signal is comparable to the input signal, it represents a distortion or degradation of the signal. The amplified signal is coming back to the microphone with a delay and with whatever "coloring" the sound system and the room give to it.

 How much amplification can you get? Why does the sound system "ring"?
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# "Ringing the System"

When the gain on a sound amplification system is turned too high, the output from the loudspeaker changes to an unpleasant, loud, usually high-pitched sound. This is the result of too much feedback, but instead of reproducing the sound being amplified, it usually produces a single pitch at the frequency which is amplified the most by the sound system/room combination.

Note that an ideal sound system responds equally to all frequencies. This not only gives a high fidelity reproduction of the sound, it also gives a higher potential acoustic gain from the amplifier system. The horizontal dashed line which represents the ideal system on the right above is still well short of the feedback level when the other system begins to ring. The procedure for filtering the frequency response to approach the ideal flat response is called equalization.

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# Inverse Square Law Assumption

In the development of a simplified model for a sound amplification system, a starting assumption is that the sound drops off according to the inverse square law. Of course this is not true in the real auditorium because one of the primary goals in auditorium acoustics is to overcome the inverse square law with natural reverberation. Nevertheless, this assumption permits the calculation of an important limiting case so that the reverberation effects in real auditoriums can be assessed by comparison.

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# Omnidirectional Assumption

In the development of a simplified model for a sound amplification system, a starting assumption is that the microphones and loudspeakers are omnidirectional, i.e., their response is equal in all directions. Of course no real microphones or loudspeakers are truly omnidirectional, but this assumption permits the calculation of an important limiting case. Under this assumption, the potential acoustic gain of an amplification system can be calculated geometrically. Such a model forms a good base for assessing the improvements which can be made with directional microphones and directional speakers.

 Numerical example Potential Acoustic Gain
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