Civil Engineering Reference
In-Depth Information
b)
a)
1 m
2
Figure 3.2
a)
Intensity: power through a surface of area 1 m
2
normal to the direction of wave propagation. b)
The intensity integrated over a closed surface gives the total emitted power of a source.
With the term
sound
intensity
is meant the sound power transmitted through a surface
terms sound intensity and sound power it is normally understood that these are time-
averaged quantities. However, for completeness we shall also introduce the instantaneous
quantities as well. The intensity is, analogous to the particle velocity, a vector quantity
and is given by the product of the sound pressure at a point and the associated particle
velocity, i.e. expressed as
2
I
()
t
=⋅
pt
()
v
()
t
(watt/m )
.
(3.28)
The time-averaged sound intensity is ideally defined by the expression
T
1
∫
I
=
lim
⋅
pt
( )
⋅
v
( ) d ,
t
t
(3.29)
T
T
T
⇒∞
0
where
T
is the measuring time, which in practice must certainly be finite. The total sound
power emitted from a given source is found by integrating the time-averaged intensity
over a surface completely enclosing the source
v
v
∫
∫
(3.30)
W
=
In
⋅
d
S
=
I
⋅
d
S
(watt),
T
T
n
where
n
denotes the unit vector normal to an element d
S
of the surface. The quantity
I
T
n
is then the component of the intensity in the normal direction, the normal time-averaged
sound intensity often being abbreviated to
normal sound intensity.
It should be noted that
this quantity is a signed one. In the same way as for the sound pressure level we define a
normal (time-averaged) sound
intensity level
as
⎡
I
⎤
T
n
L
=⋅
⎢
10 lg
(dB).
(3.31)
⎥
IT
n
I
⎣
⎦
0
