Digital Sound & Music: Concepts, Applications, & Science, Chapter 4, last updated 6/25/2013
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In Section 4.2.2.1, we looked at how the PAG is determined so that a sound engineer can know
the limits of the gain he can apply to the sound without getting feedback. You can understand
why feedback happens and how it can be prevented by applying the inverse square law.
First, we can derive an equation for the sound level that comes from the singer arriving at
the microphone at intensity vs. arriving at the listener at intensity , without sound
reinforcement. All sound levels are in decibels. By the inverse square law, the relationship
between and is this:
( *
Equation 4.18
Figure 4.40 Computing the PAG
We can also apply the inverse square law to the sound coming from the loudspeaker and
arriving at microphone at intensity vs. arriving the listener at intensity , with
reinforcement Feedback occurs where . Thus we have
( *
Equation 4.19
Subtracting Equation 4.18 from Equation 4.19, we get
( * ( *
( )
( *
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