Civil Engineering Reference
In-Depth Information
field in the sound is a superposition of plane waves. As seen from the formula, the
intensity at the boundaries differs only by the constant 4, different from the
corresponding one in a plane progressive wave. Introducing this result into Equation
(4.25)
we get
( )
2
d
p
2
p
V
W
=
⋅ +
A
⋅
.
(4.27)
2
4
ρ
c
d
t
ρ
c
00
00
Obviously, the pressure root-mean-square value here must be interpreted as a short-time
averaged variable, i.e. the averaging must be performed over a time interval much less
than the reverberation time. The general solution of this equation is given by
Ac
4
ρ
c
0
−
t
2
00
p
=
⋅ + ⋅
W
K
e
4
V
.
(4.28)
A
The constant
K
is determined by the initial conditions. We shall look into two special
cases, applying this solution.
4.5.1.1
The build-up of the sound field. Sound power determination
We now assume that the sound pressure is zero when the source is turned
on, (
, which gives
p
=
0
t
t
=
0
)
4
ρ
c
00
K
=−
⋅
V
and
A
c
⎞
(4.29)
⎛
⎜
Ac
4
ρ
0
−
t
2
00
⎟
p
=
W
1e
−
4
V
.
⎜
⎟
A
⎝
⎠
The sound will then build up arriving at a stationary value when the time
t
goes to
infinity. The RMS-value of the sound pressure becomes
4
ρ
c
2
00
p
→∞
=
W
.
(4.30)
t
A
The equation then gives us the possibility of determining the sound power emitted by a
source by way of measuring the mean square pressure in a room having a known total
absorbing area. For laboratories this type of room is called a
reverberation room
and
procedures for such measurements are found in international standards (see e.g. ISO
3741).
A couple of important points concerning such measurements must be mentioned.
As pointed out above, one has to determine the time and space averaged value of the
sound pressure squared. This is accomplished either by measurements using a
microphone (or an array of microphones) at a number of fixed positions in the room or
by a microphone moved through a fixed path in the room (line, circle etc.). One must,
however, avoid positions near to the boundaries where the sound pressure is
systematically higher than in the inner parts of the room. Waterhouse (1955) has shown
that the sound pressure level at a wall, at an edge and at a corner, respectively, will be 3,
