Effective Length of Absorptive Cylinder
Installed on the Edge of a Barrier
Mizuki INOUE※1 and Kyoji FUJIWARA※2※1※2

Yotsumoto Acoustic Design Inc.
Faculty of Design, Kyushu University

Abstract
It is common to build a barrier to reduce traffic noise.
To improve the efficiency of the barrier with keeping its
height low, an absorptive structure is often installed on
its top edge. This paper presents a study on an effective
length of absorptive cylinder, which has equivalenteffect with infinite length.

1. Introduction
Barriers are commonly used to reduce traffic noise. The
sound shielding efficiency is improved by increasing theheight of the barrier. However, high barriers present
various problems, such as their large structural load.
Therefore, various new methods have been developed.
One of those, it is the installation of an absorptive
cylinder on the barrier edge, as shown in Fig.1[1].
In the study of a 3 m height barrier constructed alongan actual expressway, a noise reduction of 2 to 3 dB
was obtained at the receiving point, where thediffraction angle was relatively large, when a cylinderof about 50 cm diameter was added on its top edge.
However, the relationship between the finite cylinder
length and its effectiveness is not fully established. It is
the purpose of this study to determine the effective
length of absorptive cylinder for road traffic noise.

2. Effect for the Incident Angle
Road traffic noise can be considered as an incoherent
line source, and it is composed of element point sources
with random phases. The sound shielding efficiency ofthe barrier for road traffic road is often estimated byintegrating the results of each point source. However,the incident angle of the acoustic wave on the absorbing
material varies with the position of each element point
source, as shown in Fig.2. That is, when sound wave
skims the surface of the cylinder, the perimeter ofabsorbing material takes various values, or when soundwave intersects the cylinder, cross section area also
takes various values. Therefore, the effect of theabsorptive cylinder depends on the incident angle. Thus,
the dependence on the incident angle of the effect wasexamined by analyzing the three-dimensional (3-D)

Tu2.F.1

Figure 1: Absorptive cylinder installed on the barrier
edge.

Figure 2: The incident angle and the effect depend oneach point source.
sound field and with a 3-D scale model experiment.
2.1. Analysis
An integral transformation method was used foranalyzing the 3-D sound field. The solution of the 3-Dsound field could be derived from the solution of twodimensional (2-D) problems by using a Fouriertransform method on the wave number axis. Using thismethod, it is possible to obtain the solution in terms of aspherical sound wave field : p( x, y, z , K ) without solving
the 3-D sound field problem directly, though solutions at
all frequencies (including imaginary frequencies) in 2-D
sound field : q ( x, y, k[ K ,α ]) are necessary. This method
was demonstrated by D. Duhamel [2][3], who calculated
the effect of barrier attenuation on a finite impedance
ground. In this work, we deduced the new integral
transform expression given in Eq.(1) for an analysis
which could also consider the internal acoustic field ofII - 1027

Figure3 : Variables in Eq(1).
Figure5 : Geometry of barrier, source and receivers
for analyzing the sound field in 2-D before integral
transform.

Figure4 : Absorptive cylinder in common use at present.
an absorptive cylinder (we used a coupled solution
method using the boundary element method [4]).
In Eq.(1), K denotes the wave number of the 3-D soundfield and α is the variable of the integral on the wave
number. β is the admittance on the boundary surface, ρis the density of the medium, and “a “ / “ p “ are indexes
corresponding to the exterior / interior sound field forthe absorbing material, respectively as shown in Fig.3.
p (x, y, z, K a , K p , β a , β p , ρ a , ρ p )=1π+∞ æçβaq ç x, y, K a2 − α 2 , K 2p − α 2 ,,1 − α 2 / K a20èöβpρp
ρa÷
,cos(αz ) dα (1),222222 ÷
1 − α / K p 1 − α / K a 1 − α / K p ÷ø∫Figure6 : Transformation from 2-D problems to 3-D.
The effectiveness of the absorptive cylinder increases
with incident angle and diffraction angle. At lowfrequency it increases rapidly at large incidence angles,
but as the frequency increases, it occurs also at lower
incidence angles and it varies almost linearly at highfrequency. Similar results are also obtained in a scalemodel experiment [5].

3. Effective Length of Absorptive Cylinder
3.1. Condition for calculation

2.2. Results
The effect produced by an absorptive cylinder wascalculated considering the structure and physicalproperty of absorbing material used in actual cylinders.
A commonly used model called “Mushroom” is shownin Fig.4, in which glass wool is used as absorbing
material. Sources and receiving points are shown inFig.5 and Fig.6. The results of the calculations areshown in Fig.7, at frequencies of 250Hz, 500Hz,
1000Hz, and only for 5 receiver points corresponding to
10~50 degree diffraction angles respectively because of
space limitations. The results are normalized withrespect to the value at zero-degree (0°) incident angle.

Now, we can determine the effective length ofabsorptive cylinder considering the effect as the functionof incident angle. We consider a barrier, an incoherent
line source, and receiving points placed as shown in
Fig.8. The lower receiving point, which is located at
18m below barrier top, is supposed large diffraction
angle such as an elevated road. And the upper, located at
3m below barrier top, is supposed not large diffraction
angle such as non-elevated road. Furthermore, level
distance of the barrier and the receiving point takes 5mpitch-distance from 5 m to 30 m. Therefore, we canobtaine various angles of diffraction. The insertion lossof a barrier with a finite length of absorptive cylinder

II - 1028

Relative Effect of Absorptive Cylinder [dB]
Relative Effect of Absorptive Cylinder [dB]
Relative Effect of Absorptive Cylinder [dB]

250Hz

2010deg
20deg
30deg
40deg
50deg

1510Diffraction angle

50-5010203040506070
Incident Angle [degree]90

Figure 8: Geometry of barrier, source and receivers forvarious diffraction angles.

500Hz

2010deg
20deg
30deg
40deg
50deg

151080edge for the incoherent line source is calculated as,z sn (γ )Diffraction angle

IL = −10 log10010203040506070Incident Angle [degree]

90

1000Hz2010deg
20deg
30deg
40deg
50deg

151080Diffraction angle

2z (γ )

ò02sn

2

| φ free ( z ) | dz(2)3.2. Results

50-50z (γ )| φWC ( z ) | dz + ò z ( γ ) | φ HB ( z ) | dz

where φ HB is the velocity potential at the receiving pointin the field diffracted by a half-plane only and is
calculated by the first approximation solution ofMacdonald[6]. φWC is the velocity potential, calculated
from φ HB plus the effect of the absorptive cylinder as thefunction of incident angle and diffraction angle. φ free isthe velocity potential at the receiving point in the freefield. The velocity potential was calculated at 1/3 octave
center frequencies between 50 and 5000Hz, considering
the atmospheric absorption as an excess attenuation [7].
Further, the insertion loss was also calculated for Aweighted road traffic noise [8]. The effect of anabsorptive cylinder of finite length is defined as thesound pressure level difference between the cases where
the absorptive cylinder is installed or not.

5-50ò010203040506070Incident Angle [degree]

8090Figure 7: Influence of the incident angle of the effect of
the absorptive cylinder for three different frequencies.

Results are shown in Fig.9 where the length at horizontal
axis denotes a half length of cylinder installed. The
results show that the effect increases with length, andconverges to certain values. The length, for which theeffect is less than 0.5dB below the value obtained for aninfinite length, is defined as the “Effective length”. Thesolid line in Fig.10 gives an effective length, it is about
80m, when the horizontal distance from the barrier to thereceiving point is 5m for upper receiving point.
Similarly, the effective length is about 130m when thehorizontal distance from the barrier is 10m. When thereceiving point is far from the barrier, a longer length isnecessary. The same result is obtained for lower

II - 1029

The effective length (L [m]) could be expressed as afunction of the distance (x [m]) between the receiverpoint and the barrier as shown in the following equationand represented by the dotted line in Fig.10.

Effect of Absorptive Cylinder [dB]

3.0
2.5
2.0
1.5
1.0
0.5
0.00

Effect of Absorptive Cylinder [dB]

0.0

4. Conclusions

5000

It is shown that the effect of an absorptive cylinder forelement point sources depends on the incident angle andthat the effect increases with this incident angle.
The effective length of absorptive cylinder for roadtraffic noise reduction was calculated considering theinfluence of the incident angle on the effect. The results
show that the effective length depends on the position ofthe receiver point and it could be expressed as a functionof the distance between the receiver point and the barrier.

Distance of Receiver Point
from the Barrier
5m
10m
15m
20m25m[ for lower receiving point ]
30m
0

1000
2000
3000
4000
Length of Absorptive Cylinder [m]5. References

5000

Effective Length of Absorptive Cylinder [m]Figure 9: Effect of absorptive cylinder for incoherent
line source.
1000
900
800

for
forupperplanereceiving
road point
forpoint –polynomial
approximation
forupperplanereceiving
road-polynomial
approximationforreceiving
point
forlower
elevatedroadforreceiving
point –polynomialapproximation
approximation
forlower
elevatedroad-polynomial

700
600
500
400
300
200
10005(4)

1000
2000
3000
4000
Length of Absorptive Cylinder [m]2.00.5

L = 0.0078 x3 − 0.8623 x 2 + 32.738 x + 109.78
for lower receiving point

The effective length increases with the distance of thereceiving point from the barrier, but converges to somevalue.

2.51.0(3)Distance of Receiver Point
from the Barrier
5m
10m
15m
20m
25m
[ for upper receiving point ]30m

3.01.5

L = 0.0034 x3 − 0.3778 x 2 + 15.254 x + 11.797
for upper receiving point

1015202530
Distance of Receiving Point from the Barrier [m]Figure 10: Effective length of absorptive cylinder.
receiving point, but longer lengths are necessary.
Because the effect of the cylinder is more important,thus a long length is necessary to obtain an effectequivalent to that of an infinite length.

[1] K. Fujiwara and N. Furuta, "Sound Shielding
Efficiency of a Barrier with a Cylinder at the Edge.'',Noise Control Eng. J. , 37:5-11, 1991.
[2] D.Duhamel, " Efficient Calculation of the ThreeDimensional Sound Pressure Field around a NoiseBarrier. '', J.Sound Vib., 197:547-571, 1996.
[3] D.Duhamel and P.Sergent, " Sound Propagation
over Noise Barriers with Absorbing Ground. '',J.Sound Vib., 218:799-823, 1998.
[4] A. F. Seybert, C. T. R. Cheng and T. W. Wu " Thesolution of coupled interior/exterior acoustic
problem using the boundary element method. ", J.
Acoust. Soc. Amer., Vol. 88, 1990, 1612-1618.
[5] M. Inoue and K. Fujiwara, "A Study on Effective
Length of Absorptive Cylinder Installed on theEdge of a barrier. '', J.Aoust.Soc.Jp., 59:141-143,
2003. in Japanese[6] J.J. Bowman, T.B.A. Senior and P.L.E. Uslenghi,
Electromagnetic and Acoustic Scattering by Simple
Shapes, North-Holland Publishing Co., Amsterdam,
330-335 1969.
[7] " Acoustics -- Attenuation of sound during
propagation outdoors -- Part1 : Calculation of theabsorption of sound by the atmosphere.", JIS Z
8738 (1999) in Japanese , ISO 9613-1 (1993)[8] Research Committee of Road Traffic Noise inAcoustical Society of Japan," ASJ Prediction Model1998 for Road Traffic Noise Report.", J.Acoust.
Soc.Jp., 55:281-324, 1999. in Japanese

II - 1030