PROCEEDINGS of the23rd International Congress on Acoustics
9 to 13 September 2019 in Aachen, Germany

A boundary virtual sound barrier system for sound radiation throughopenings with double-layer secondary sources and error
microphonesShuping WANG1; Xiaojun QIU2; Jiancheng TAO3
1

University of Technology Sydney, Australia

2

University of Technology Sydney, Australia
3

Nanjing University, ChinaABSTRACT
According to Huygens’ principle, sound radiation through an opening can be completely reduced with asufficient number of secondary sources over the entire opening, but secondary sources in the middle of theopening affect the functionalities of openings. In this paper, a boundary virtual sound barrier system isproposed. By applying double-layer secondary sources and error microphones both at the edge of the opening,such a system can achieve satisfactory noise reduction performance over a wide frequency band without
blocking the opening. Experiments are carried out in the anechoic chamber to support the numericalsimulation results.
Keywords: Virtual sound barrier, Boundary, Opening

1. INTRODUCTION
Openings are widely used in our lives to keep natural ventilation and lighting of buildings, but they
provide sound transmission paths and result in the noise radiation problem at the same time. The active
noise control (ANC) technique is a good supplement to traditional passive noise reduction methods incontrolling sound radiation through openings because it performs better in low frequency range while
passive noise control is more effective for high frequencies, and unlike passive noise control methods,
it does not require the opening to be sealed (1).
Based on Huygens’ principle, it has been proposed in previous work to implement secondary
sources over the entire opening, and it is demonstrated as an effective way to reduce sound radiation
through openings (2, 3); however, secondary sources in the middle of the opening still block theopening and affect its functionalities. It is desired that the ANC system be implemented at the edge ofthe opening to keep the opening completely clear. Wang et al. investigated the performance of adouble-layer secondary source system at the edge of the opening, and found that it outperforms thesingle-layer system with the same number of secondary sources and there exists an upper-limitfrequency for such a double-layer system, which is related to the size of the opening (4, 5). Bhan et al.
also worked on the boundary layout of secondary sources and found that it could attenuate noise as
effectively as the fully-glazed window (6).
In addition to the configuration of secondary sources, error sensing is another important part of
ANC. To achieve global control, error microphones should provide signals proportional to the soundpower. One way to obtain the sound power is to measure the sound intensity in the near field, butminimizing the near-field sound intensity suffers from the fact that it is a signed quantity (7). Qiu et al.
compared eight different cost functions and found that the optimal cost function is the sum of theweighted mean active intensity in the direction normal to the surface surrounding the primary andsecondary sources (8). In most cases, it is difficult to find the optimal locations for error microphones
in the near field, and they are usually distributed over the entire opening to reduce noise radiation
through the opening, which affect the functionalities of the opening as well (4).
1shuping.wang@uts.edu.au
xiaojun.qiu@uts.edu.au
3
jctao@nju.edu.cn
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In our previous work, a double-layer boundary error sensing arrangement was proposed andnumerical simulations showed that the double-layer arrangement performs better than single-layer one(9). More detailed numerical simulations are carried out in this paper to explore the rules of active
control with double-layer error microphones at the edge. Experiments conducted in the anechoic
chamber are presented to support the numerical simulation results.

2. MODELFigure 1 shows a schematic diagram of the proposed virtual sound barrier system at the edge of thecavity opening. In the system, secondary sources are distributed in two layers at the edge and they havethe same coordinates in the x-y plane. Error microphones have similar layouts to the secondary sources
and they are located above the secondary sources. The primary noise source is inside the open cavity.
It is assumed that all the five walls are rigid, so sound outside is solely that transmitted through theopening.

Figure – 1 The schematic diagram of the virtual sound barrier system at the edge of the cavity
opening
As the opening is the only sound transmission path from inside the cavity to the outside, the soundpower of the system can be calculated as an integral of sound intensity over the entire opening S. The
sound power without active control isWoff

1
Re ^ ppo*vpo ` dS ,
2 ³³
S

(1)

where ppo and v po are the primary sound pressures and particle velocities at the opening. The soundpower with active control is the sum of the contributions of the primary source and all the secondary
sourcesWon

1
Re ^[ ppo  pso ]*[vpo  vso ]` dS ,
2 ³³
S

(2)

where pso and vso are the secondary sound pressures and normal particle velocities at the opening.
The noise reduction of the system is defined as the difference of the sound power level without andwith control.

NR 10 log103282

Woff.
Won

(3)

3. NUMERICAL SIMULATIONSIn the numerical simulations, the size of the open cavity is 0.432 m u 0.67 m u 0.598 m, and there
are a total of 20 secondary sources at the edge of z = 0.448 m and z = 0.498 m planes. Threeconfigurations of error microphones are investigated: single-layer, double-layer and evenly distributed,
and their positions in the x-y plane are shown in Fig. 2. The single-layer and evenly distributed error
microphones are at z = 0.588 m plane and the double-layer error microphones are at z = 0.568 m and z= 0.588 m planes. To prevent the system from being underdetermined, more error microphones thansecondary sources are used, and the number is 32 here. The primary source is a monopole point source
located at (0.1, 0.1, 0.1) m inside the open cavity with a strength of 10 4 m3 /s.

Figure – 2 The positions of error microphones in the x-y plane: (a) the single-layer configuration, (b)the double-layer configuration, (c) the evenly distributed configuration
The sum of the squared sound pressures at the error points is used as the cost function to obtain thestrengths of secondary sources (10). The noise reduction of the system is calculated with Eq. (3).
Figure 3 shows the sound power levels with and without control under the three configurations of error
microphones. It is clear that the system with error microphones evenly distributed over the entire
opening achieves the best noise reduction performance, and the one with double-layer error
microphones outperforms that with single-layer ones at all the frequencies below 1000 Hz.

Figure – 3 The sound power levels with and without control when 20 secondary sources are arranged
in double-layer configuration

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The effect of the heights of double-layer error microphones on the noise reduction performance isalso investigated. There are still a total of 32 error microphones. Figure 4(a) shows the sound power
levels with and without control when the distance between the two layers is fixed as 0.02 m, and it
can be seen that the noise reduction performance improves when the error microphones are closer tothe opening. If one of the layers is fixed at z = 0.518 m, and the other layer is placed at different
heights, the sound power levels with and without control are shown in Fig. 4(b). Although all theconfigurations achieve satisfactory noise reductions below 1000 Hz in Fig. 4(b), there are still small
differences between them and the system with the other layer closer to the opening performs thebest.

(a)

(b)
Figure – 4 The sound power levels with and without control with 20 double-layer secondary sourcesand 32 double-layer error microphones: (a) the distance between two layers of error microphones isfixed as 0.02 m, (b) one of the layers is fixed at z = 0.518 m plane
Double layer error microphones also perform better than single-layer ones when the primarysound field is complicated. The primary source is simulated as 8 monopole point sources in a 0.1 m
u 0.1 m u 0.1 m volume with random amplitudes and phases. Figure 5 shows the results for 32
single-layer and double-layer error microphones. It is clear that the system with double-layer error
microphones achieves higher noise reductions than that with single-layer ones.

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Figure – 5 The sound power levels with and without control with 20 double-layer secondary sourcesand 32 double-layer error microphones when the primary sound field is complicated

4. EXPERIMENTS
Experiments were carried out in the anechoic chamber of Nanjing University. The open cavity wasconstructed with five 20 mm-thick acrylic glass plates and the size is 0.432 m u 0.67 m u 0.598 m. A
total of 32 secondary sources were implemented at the edge of z = 0.448 m and z = 0.548 m planes. The
primary source was a loudspeaker inside the open cavity which generated tonal sound field. Three
configurations of error microphones: evenly distributed, single-layer and double-layer wereinvestigated and the pictures of the three experimental setups are shown in Figs. 6(a)-(c). The
single-layer and evenly distributed error microphones were installed in the opening plane. The
double-layer error microphones were installed at the opening and the plane 0.02 m below it. The
waveform synthesis algorithm was used in the experiments; it applied the internally synthesized tonal
signal as the reference signal, so no reference microphone was required here (11). As shown in Fig.
6(d), ten microphones fixed on a frame with a radius of 1.5 m were used to measure the sound power
levels with and without control (12).

(a)

(b)

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(c)
(d)
Figure – 6 Pictures of the experimental setup: (a) evenly distributed error microphones, (b)single-layer error microphones, (c) double-layer error microphones, (d) the panoramic view in theanechoic chamber
The sound power levels measured in the experiments with and without control are shown in Fig.
7(a) and the corresponding numerical simulation results on the same configurations are shown in Fig.
7(b). It can be seen from Fig. 7(a) that the system with evenly distributed error microphones achieve
the best performance among the three configurations and the double-layer error microphones
perform slightly better than the single-layer ones.
It can be found by comparing Fig. 7(a) with Fig. 7(b) that the advantage of the double-layer error
microphones over single-layer ones in the experiments is not as apparent as that in the numericalsimulations. There are two possible reasons. One is that the error microphones used in theexperiments have different sensitivities, and it is actually the sum of the squared electric signals
picked up by the error microphones instead of the sum of the squared sound pressures at error points
that is minimized in the experiments, which makes the noise reduction performance different fromthat in the numerical simulations. The other possible reason is that the error microphones in theexperiments were not rigorously fixed at the positions they were supposed to be at. The reasons will
be checked in the future. Future work also includes finding a proper way to pick up the reference
signal, especially for practical sound fields.

(a)

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(b)
Figure – 7 The sound power levels with and without control: (a) experimental results, (b)corresponding numerical simulation results

5. CONCLUSIONS
A boundary virtual sound barrier system with both double-layer secondary sources and error
microphones at the edge is proposed to reduce sound radiation through openings. Numericalsimulations show that similar to the conclusions for secondary source configurations, the system withdouble-layer error microphones performs better than that with single-layer ones, and the conclusion isstill valid for complicated primary sound fields. It is also found that the performance of the systemwith double-layer error microphones improves if the error microphones are closer to the opening.
Experimental results in the anechoic chamber show that the system with double-layer error
microphones perform slightly better than that with single-layer ones, and the advantage is not asapparent as that in the numerical simulations. The reasons might be the different sensitivities andinaccurate positions of error microphones in the experiments.

ACKNOWLEDGEMENTS
This research was supported by the National Science Foundation of China (11874218, 11474163)
and under the Australian Research Council’s Linkage Projects funding scheme (LP140100987). Theauthors would also like to thank Mr. Kang Wang for his help with the experiments.

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