Introduction to Acoustics

Sound Propagation in the Atmosphere 4.8 Wind and Temperature Gradient Effects on Outdoor Sound 133
where
ς ′ |ς|
= .
1 −|ς|z>
Figure 4.16 shows that, for source and receiver
heights of 1 m and a normalized speed of sound gradient
of 0.0001 m−1 , the distance to the shadow zone
boundary is about 300 m. As expected the distance to
the shadow-zone boundary is predicted to increase as
the source and receiver heights are increased.
A good approximation of (4.36), for the distance to
the shadow zone, when the source is close to the ground
and ζ is small, is
�
2c0
rc =
− dc
�1/2 ��
hs +
dz
� �
hr , (4.51)
where hs and hr are the heights of source and receiver
respectively and dc/dz must be negative for
a temperature-induced shadow zone.
Conditions of weak refraction may be said to exist
where, under downward-refracting conditions, the
ground-reflected ray undergoes only a single bounce
and, under upward-refracting conditions, the receiver is
within the illuminated zone.
When wind is present, the combined effects of temperature
lapse and wind will tend to enhance the shadow
zone upwind of the source, since wind speed tends to increase
with height. Downwind of the source, however,
the wind will counteract the effect of temperature lapse,
Distance to shadow zone boundary (km)
3.0
2.5
2.0
1.5
1.0
0.5
10m
3.5m
1m
0
0 2 4 6 8 10
Normalized sound speed gradient (10 5 m –1 )
Fig. 4.16 Distances to shadow-zone boundaries for linear
speed of sound gradient based on (4.36) assuming equal
source and receiver heights: 1 m (solid line); 3.5m(broken
line) and 10 m (dot–dash line)
and the shadow zone will be destroyed. In any case, an
acoustic shadow zone is never as complete as an optical
one would be, as a result of diffraction and turbulence.
In the presence of wind with a wind speed gradient of
du/dz, the formula for the distance to the shadow-zone
boundary is given by
�
2c0
rc =
du
dz cos β − dc
�1/2 ��
hs +
dz
� �
hr , (4.52)
where β is the angle between the direction of the wind
and the line between source and receiver.
Note that there will be a value of the angle β, (say
βc), given by
du
dz cos βc = dc
dz
or
βc = cos −1
� � �
dc du
dz dz
(4.53)
at and beyond which there will not be a shadow zone.
This represents the critical angle at which the effect of
wind counteracts that of the temperature gradient.
4.8.2 Meteorological Classes
for Outdoor Sound Propagation
There is a considerable body of knowledge about meteorological
influences on air quality in general and the
dispersion of plumes from stacks in particular. Plume
behavior depends on vertical temperature gradients and
hence on the degree of mixing in the atmosphere. Vertical
temperature gradients decrease with increasing wind.
The stability of the atmosphere in respect to plume dispersion
is described in terms of Pasquill classes. This
classification is based on incoming solar radiation, time
of day and wind speed. There are six Pasquill classes
(A–F) defined in Table 4.2.
Data are recorded in this form by meteorological stations
and so, at first sight, it is a convenient classification
system for noise prediction.
Class A represents a very unstable atmosphere with
strong vertical air transport, i. e., mixing. Class F represents
a very stable atmosphere with weak vertical
transport. Class D represents a meteorologically neutral
atmosphere. Such an atmosphere has a logarithmic wind
speed profile and a temperature gradient corresponding
to the normal decrease with height (adiabatic lapse rate).
A meteorologically neutral atmosphere occurs for high
wind speeds and large values of cloud cover. This means
that a meteorologically neutral atmosphere may be far
Part A 4.8