Digital Sound & Music: Concepts, Applications, & Science, Chapter 4, last updated 6/25/2013
( ) ( *
where is the initial distance from the sound, is the new distance from the sound, is the
intensity of the sound at the microphone in decibels, and is the intensity of the sound at the
listener in decibels
Equation 4.13 Inverse square law
What this means in practical terms is the following. Say you have a sound source, a
singer, who is a distance from the microphone, as shown in Figure 4.19. The
microphone detects her voice at a level of dBSPL. The listener is a distance
from the singer. Then the sound reaching the listener from the singer has an intensity of
( *
( * ( *
Notice that when the logarithm gives a negative number, which makes sense because the
sound is less intense as you move away from the source.
The inverse square law is a handy rule of thumb. Each time we
double the distance from our source, we decrease the sound level by 6 dB.
The first doubling of distance is a perceptible but not dramatic decrease in
sound level. Another doubling of distance (which would be four times the
original distance from the source) yields a 12 dB decrease, which makes the
source sound less than half as loud as it did from the initial distance. These
numbers are only approximations for ideal free-field conditions. Many other
factors intervene in real-world acoustics. But the inverse square law gives a
general idea of sound attenuation that is useful in many situations.
4.2.2 Acoustic Considerations for Live Performances Potential Acoustic Gain (PAG)
When setting up for a live performance, an important function of the sound
engineer operating the amplification/mixing system is to set the initial
sound levels.
The acoustic gain of an amplification system is the difference
between the loudness as perceived by the listener when the sound system is
turned on as compared to when the sound system is turned off. One goal of
the sound engineer is to achieve a high potential acoustic gain, or PAG
the gain in decibels that can be added to the original sound without causing
feedback. This potential acoustic gain is the entire reason the sound system is installed and the
sound engineer is hired. If you can’t make the sound louder and more intelligible, you fail as a
sound engineer. The word “potential” is used here because the PAG represents the maximum
gain possible without causing feedback. Feedback can occur when the loudspeaker sends an
audio signal back through the air to the microphone at the same level or louder than the source.
In this situation, the two similar sounds arrive at the microphone at the same level but at a
Working with
Acoustic gain
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