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K
w
1
f
f
w
for
for
f
f
f
w
f
w
,
K
l
1
f
f
l
for
for
f f
l
f f
l
f
w
c a *
2( w cos
)
2
,
f
l
c a *
2
2 l
where
a*
d
2( d
inc
inc
d
refl
d
refl
)
If we assume energy conservation, then we must also assume that the energy which is not
reflected specularily has been diffracted - scattered due to diffraction. This leads to the
following formulae for our scattering coefficient due to diffraction:
s
d
1
KwKl
(1
se
)
In order to compensate for the extra diffraction which occurs when a reflection appears close
to an edge of a free surface, the specular component is reduced by a factor 1-s e. The edge
scattering coefficient is defined to be 0.5 if the reflection occurs at the edge of a surface
saying that half of the energy is scattered by the edge and the other half is reflected from the
surface area. If the reflection point is far from the edge, the edge scattering becomes zero –
initial investigations suggests that edge scattering can be assumed to zero when the distance
to the edge is greater than approximately one wave length, therefore we define the edge
scattering coefficient as:
0
se
0.5(1
d
edge
cos
c
f
)
for
for
d
d
edge
edge
cos
cos
c
f
c
f
As can be seen, scattering caused by diffraction is a function of a number of parameters some
of which are not known before the actual calculation takes place. An example is that oblique
angles of incidence lead to increased scattering whereas parallel walls lead to low scattering
and sometimes flutter echoes. Another example is indicated by the characteristic distance a*,
if source or receiver is close to a surface, this surface may provide a specular reflection even if
its small, on the other hand if far away it will only provide scattered sound, s d ≈1.
log(E)
fl
fw
Log(frequency)
Figure 6-4. Energy reflected from a free suspended surface given the dimensions l∙w. At
high frequencies the surface reflects energy specularily (red), at low frequencies, energy
is assumed to be scattered (blue). fw is the upper specular cut off frequency defined by
the shortest dimension of the surface, fl is the lower cutoff frequency which is defined by
the length of the surface.
Boundary walls and interior margin
As long as surfaces are truly freely suspended surfaces, they will act as effective diffusers
down to infinitely low frequencies. For surfaces which are elements in the boundary of the
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