Civil Engineering Reference
In-Depth Information
As derived in Chapter 3 (section 3.5.1.1), the RMS-value of the sound pressure at a
given frequency may be expressed as
1
p
ˆ
2
⎡
⎤
⎥
2
,
i
px
()
=
1
+
R
+
2
R
cos(2
kx
δ
+
)
(5.1)
⎣
p
p
⎦
2
where
R
p
is the pressure reflection factor having phase angle δ.
Loudspeaker
Probe
Specimen
Figure 5.3
Sketch of the set-up for the “classical” standing wave tube measurement method.
From the ratio of the maximum and the minimum sound pressure amplitudes, these
amplitudes are given by
ˆ
p
()
i
⎡
⎤
p
=
1
+
R
⎣
p
⎦
max
2
ˆ
(5.2)
p
()
i
⎡
⎤
and
p
=
1
−
R
,
⎣
p
⎦
min
2
we may then determine the modulus of the pressure reflection factor
R
p
. The phase angle
δ is determined by the position of the first minimum pressure close to the specimen. (Can
you set up the expression for this phase angle using Equation
(5.1)
?). From these data
both the input impedance
Z
g
and the absorption factor α are determined from the
equations
1
+
R
1
+
R
p
p
Z
=
ρ
c
=
Z
(5.3)
g
0
0
0
1
−
R
1
−
R
p
p
and
Z
Z
⎧
⎪
⎨
⎪
⎩⎭
g
4Re
0
α
=
(5.4)
.
2
Z
Z
⎧
⎪
⎪
g
g
+
2Re
+
1
⎨
⎪
⎩⎭
Z
Z
0
0
A sketch of the sound pressure level, given by the expression
