Digital Sound & Music: Concepts, Applications, & Science, Chapter 4, last updated 6/25/2013
different phase. The first frequency from the loudspeaker to combine with the source at a 360
degree phase relationship is reinforced by 6 dB. The 6 dB reinforcement at that frequency
happens over and over in an infinite loop. This sounds like a single sine wave that gets louder
and louder. Without intervention on the part of the sound engineer, this sound continues to get
louder until the loudspeaker is overloaded. To stop a feedback loop, you need to interrupt the
electro-acoustical path that the sound is traveling by either muting the microphone on the mixing
console or turning off the amplifier that is driving the loudspeaker. If feedback happens too many
times, you'll likely not be hired again.
The equation for PAG is given below.
where is the distance from the sound source to the microphone,
is the distance from the sound source to the listener,
is the distance from the microphone to the loudspeaker, and
is the distance from the loudspeaker to the listener
Equation 4.14 Potential acoustic gain (PAG)
PAG is the limit. The amount of gain added to the signal by the sound engineer in the sound
booth must be less than this. Otherwise, there will be feedback.
In typical practice, you should stay 6 dB below this limit in order to avoid the initial
sounds of the onset of feedback. This is sometimes described as sounding “ringy” because the
sound system is in a situation where it is trying to cause feedback but hasn’t quite found a
frequency at exactly a 360 phase offset. This 6 dB safety factor should be applied to the result
of the PAG equation. The amount of acoustic gain needed for any situation varies, but as a rule
of thumb, if your PAG is less than 12 dB, you need to make some adjustments to the physical
locations of the various elements of the sound system in order to increase the acoustic gain. In
the planning stages of your sound system design, you’ll be making guesses on how much gain
you need. Generally you want the highest possible PAG, but in your efforts to increase the PAG
you will eventually get to a point where the compromises required to increase the gain are
unacceptable. These compromises could include financial cost and visual aesthetics. Once the
sound system has been purchased and installed, you'll be able to test the system to see how close
your PAG predictions are to reality. If you find that the system causes feedback before you're
able to turn the volume up to the desired level, you don;t have enough PAG in your system. You
need to make adjustments to your sound system in order to increase your gain before feedback.