Civil Engineering Reference
In-Depth Information
•
The sound scattering objects are assumed to be point like and the energy of the
incident wave is scattered evenly in all directions.
•
The scattering phenomenon follows a Poisson process. The energy emitted by the
source is sent out in discrete quantities as “phonons” or sound packages having
energy
W
⋅Δ
t
, where
W
is the sound power of the source.
120
110
100
SURFACE
Flat - Anal.
Flat - FEM
Diffusor - FEM
90
0
1
2
3
Angle (radian)
Figure 4.19
Total sound pressure level as a function of angle calculated on the circle with radius
r
equal one
meter; situation as depicted in
Figure 4.18
. The source (S) power is equal to 1.0 W.
Thick solid line - diffuser
surface (FEM). Thin solid line - flat surface (FEM). Dashed line - flat, infinitely large surface (analytical).
The validity of the first hypothesis will depend on the ratio of the dimensions of the
scattering object and the actual wavelength. Initially assuming that an object scatters
sound, not only reflects sound in a specular way, we shall put up a limit on the
relationship between a typical dimension
D
and the wavelength
λ
, demanding that
D/
λ
>
1/2
π
.
From the second hypothesis follows that the probability density
P
k
of a phonon
hitting a number
k
scattering objects within a time interval
t
k
is given by
k
−
qc t
(
)
e
⋅
qc t
0
k
0
k
Pct
(
)
=
,
(4.70)
k
0
k
k
!
where
c
0
is the usual wave speed and
q
is the average
scattering cross section
per unit
room volume, a quantity also denoted the scattering frequency.
The determination of
q
is difficult for scattering objects having a complicated
shape. A common practice is equalizing the scattering effect (at high frequencies) of an
object having a total surface area
S
by the one offered by a sphere of equal surface area.
The average scattering cross section may then be expressed as
