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

( * ( *

( )

( *