Page 64 - Master Handbook of Acoustics

For example, if a sound-pressure level of 80 dB is measured at 10 ft, we can determine the sound-
pressure level at 15 ft:

20 log 10/15 = −3.5 dB, and the level is 80 − 3.5 = 76.5 dB.

Similarly we can determine the sound-pressure level at 7 ft:

20 log 10/7 = +3.1 dB, and the level is 80 + 3.1= 83.1 dB.

This is only true for a free field in which sound diverges spherically, but this procedure may be
helpful for rough estimates under other conditions.
If a microphone is 5 ft from a singer and a VU meter in the control room peaks at +6 dB, moving
the microphone to 10 ft would bring the reading down approximately 6 dB. The 6-dB figure is

approximate because these distance relationships hold true only for free-field conditions. In practice,
the effect of sound energy reflected from walls would change the doubling of distance relationship to
something less than 6 dB.
An awareness of these relationships helps estimate acoustical situations. For example, a doubling

of the distance from 10 to 20 ft would, in free space, be accompanied by the same sound-pressure
level decrease, 6 dB, as for a doubling from 100 to 200 ft. This accounts for the great carrying power
of sound outdoors.
Even at a distance, not all sound sources behave as point sources. For example, traffic noise on a
busy road can be better modeled as many point sources cumulatively acting as a line source. Sound
spreads in a cylinder around the line. In this case, sound intensity is inversely proportional to the

distance from the source. Doubling the distance from r to 2r reduces the intensity I to I/2. This is a
decrease of 3 dB for every doubling of distance from the line source, or an increase of 3 dB for every
halving of distance from the line source.

Sound Fields in Enclosed Spaces

Free fields exist in enclosed spaces in anechoic circumstances. However, in most rooms, in addition
to the direct sound, reflections from the enclosing surfaces affect the way sound level decreases with
distance. No longer does the inverse square law or the inverse distance law describe the entire sound
field. In a free field, we can calculate sound level in terms of distance. In contrast, in a perfectly
reverberant sound field, the sound level is equal everywhere in the sound field. In practice, rooms
yield a combination of these two extremes, with both direct sound and reflected sound.

For example, assume that there is a loudspeaker in an enclosed space that is capable of producing
a sound-pressure level of 100 dB at a distance of 4 ft. This is shown in the graph of Fig. 3-3. In the
region very close to the loudspeaker, the sound field is in considerable disarray. The loudspeaker, at
such close distances, cannot be considered a point source. This region is called the near field. In the

near field, sound level decreases about 12 dB for every doubling of distance. This near-field region
(not to be confused with “near-field” or “close-field” studio monitoring) is of limited practical
interest.