Page 109 - The Master Handbook Of Acoustics

84 CHAPTER FOUR

undiffracted, unrefracted, undiffused, and not subjected to resonance
effects. These are all hazards that could (and do) face a simple ray of
sound leaving a source.
Free space must not be confused with cosmological space. Sound
cannot travel in a vacuum; it requires a medium such as air. Here, free
space means any air space in which sound acts as though it is in the
theoretical free space. Limited free space can even exist in a room
under very special conditions.

Sound Divergence

The point source of Fig. 4-1 radiates sound at a fixed power. This
sound is of uniform intensity (power per unit area) in all directions.
The circles represent spheres having radii in simple multiples. All of
the sound power passing through the small square area at radius d also
passes through the areas at 2d, 3d, 4d, etc. This increment of the total
sound power traveling in this single direction is spread over increas-
ingly greater areas as the radius is increased. Intensity decreases with
2
distance. As the area of a sphere is 4πr , the area of a small segment on
the surface of the sphere also varies as the square of the radius. Dou-
1
bling the distance from d to 2d reduces the intensity to 4, tripling the
1
distance reduces the intensity to 9, and quadrupling the distance
1
reduces intensity to 16. Intensity of sound is inversely proportional to
the square of the distance in a free field.
Intensity of sound (power per unit area) is a difficult parameter to
measure. Sound pressure is easily measured. As intensity is propor-
tional to the square of sound pressure, the inverse square law (for
intensity) becomes the inverse distance law (for sound pressure). In
other words, sound pressure varies inversely as the first power of the
distance. In Fig. 4-2, the sound-pressure level in decibels is plotted
against distance. This illustrates the basis for the common and very
useful expression, 6 dB per doubling of the distance that, again,
applies only for a free field.
Examples: Free-Field Sound Divergence

When the sound-pressure level L 1 at distance d 1 from a point source
is known, the sound-pressure level L 2 at another distance d 2 can be
calculated from: