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

Formation of local quiet zones using the length-limited parametric
array loudspeaker
Yue WANG; Ruicong LI; Chuang SHI; Youxin LV
University of Electronic Science and Technology of China, Chengdu, China
Corresponding email: shichuang@uestc.edu.cn

ABSTRACTThis paper presents a preliminary numerical study on the formation of local quiet zones using the lengthlimited parametric array loudspeaker (PAL). The PAL is a directional sound device using the nonlinear
acoustic effect to generate an audio beam in air. The length-limited PAL aims to control the length of theaudio beam by using two different ultrasonic carriers. The sound propagation curve and radiation pattern of
the length-limited PAL are theoretically distinct from those of the conventional loudspeaker. Therefore, thelocal quiet zones formed by the length-limited PAL is of sufficient interest before any practical deploymentof the length-limited PAL in active noise control (ANC). For comparison, the local quiet zones formed by
the conventional loudspeaker and the normal PAL are also obtained and examined in the numerical simulation.
Keywords: Numerical simulation, Parametric array loudspeaker, Active noise control

1. INTRODUCTION
The PAL is a directional sound source using the nonlinear acoustic effect to generate an audio beamin air (1). It is often built up with a driver circuit and an ultrasonic emitter. The driver circuit modulates
audio input signals on an ultrasonic carrier and amplifies the modulated signal to be transmitted by
the ultrasonic emitter. The principle of the PAL is provided by the nonlinear acoustic effect: when twoultrasonic frequencies are transmitted into a nonlinear medium, the difference frequency is generated
in a narrow beam, whose pattern is similar to that of an end-fire array (2). Although air is a weak
nonlinear medium, the nonlinear acoustic effect is still sufficient to be applied in many sound field
control applications (3).
The ANC creates a quiet zone by inferring the noise wave with an anti-noise wave (4). In a freespace, the formation of a local quiet zone leads to the spillover problem, resulting in increased noiselevels outside the quiet zone. It is believed that using a directional sound source to transmit the antinoise wave can solve the spillover problem.
Brooks, Zander and Hansen investigated the feasibility of using the PAL in ANC in 2005 (5). They
concluded three practical concerns, which were (i) the PAL had a weak low-frequency response andsevere harmonic distortion; (ii) the precise control of amplitude and phase required for ANC wasdifficult to achieve; (iii) the ultrasonic exposure of the PAL has yet to be evaluated. However, several
successful experiments of using PALs in ANC have been reported recently (6, 7). The noise frequency
typically ranges from 500 Hz to 2.5 kHz.
The length-limited PAL has been proposed to use two carrier frequencies in order for the length ofthe difference frequency beam to be shortened (8, 9). Dedicated modulation methods are important
for the difference frequency beam to be confined in the relative near field of the ultrasonic emitter.
The use of the length-limited PAL in ANC has been experimentally investigated (10). However, thelocal quiet zones formed by the length-limited PAL needs to be examined further.

2. NUMERICAL CONFIGURATIONThis paper presents a preliminary numerical study of forming local quiet zones using the length limited PAL. The numerical simulation is carried out in a 0.4ͺͺ ൈ ͲǤͶͺͺ two dimensional space,55

which is surrounded by perfect matched layers to remove reverberation. The space is divided into
488ൈ488 grids. Each side of the grid is 1 mm. The noise frequency is fixed at 1 kHz. The speed ofsound and the nonlinear coefficient of air are set to 343.13 m/s and 1.2, respectively. The numericalsimulation code is modified from the k-wave toolbox (11).
2.1 Primary Noise Sources
Two different positions of the primary noise source are simulated. The diameter of the primarynoise source is 2 cm, which is approximately the size of a miniature speaker. Figure 1 shows the soundpressure distributions of the primary noise sources. The center of the simulation space is calibrated to60 dB.
(a) Noise source on the right(b) Noise source on the top

Figure 1 – Sound pressure distributions of primary noise sources
2.2 Linear Secondary Sources
Two types of linear secondary sources are simulated. Both sources are placed on the left withdiameters of 2cm and 10cm, respectively. Figure 2 shows the sound pressure distributions of the linear
secondary sources. The initial phase and amplitude are controllable, in order for the noise cancellation
to be achievable at any particular position.
(a) 2 cm loudspeaker(b) 10 cm loudspeaker

Figure 2 –Sound pressure distributions of the linear secondary sources
2.3 Nonlinear Secondary Sources
Three types of nonlinear secondary sources are simulated. They are the conventional PAL using acarrier of 40 kHz, the conventional PAL using a carrier of 90 kHz, and the length -limited PAL. All ofthem adopt the double sideband modulation.
The conventional PAL using a carrier of 40 kHz transmits a modulated ultrasonic sound, which isgiven by‫݌‬ଵ ሺ‫ݐ‬ሻ ൌ ܲଵ ሾͳ ൅ ݉‫ݔ‬ሺ‫ݐ‬ሻሿ ሺʹߨ݂ଵ ‫ݐ‬ሻ,(1)where ܲଵ is the initial pressure; ݂ଵ ൌ ͶͲ kHz is the carrier frequency; ݉ ൌ ͲǤ͹ is the modulationindex; and ‫ݔ‬ሺ‫ݐ‬ሻ is the input sine tone at 1 kHz.

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The modulated signal of the conventional PAL using a carrier of 90 kHz is written as(2)‫݌‬ଶ ሺ‫ݐ‬ሻ ൌ ܲଶ ሾͳ െ ݉‫ݔ‬ሺ‫ݐ‬ሻሿ ሺʹߨ݂ଶ ‫ݐ‬ሻwhere ܲଶ is the initial pressure; ݂ଶ ൌ ͻͲ kHz is the carrier frequency. Note that the sign in front of
the modulation index has been changed.
In order for the difference frequency beams resultant from different carrier frequencies can cancel
each other in the far field, their initial pressure levels have to obey with the following relation:(3)ܲଵΤܲଶ ൌ ඥߙଵΤߙଶ,where ߙଵ and ߙଶ are the absorption coefficients (12). Figure 3 shows the sound pressure distributionsof the nonlinear secondary sources.
(a) PAL using a 40 kHz carrier(b) PAL using a 90 kHz carrier(c) Length-limited PAL

Figure 3 – Sound pressure distributions of the nonlinear secondary sources
2.4 Active Noise Control
Practical implementations of ANC may involve a complicated procedure of adaptive filtering andmodeling. However, in the numerical simulation, ANC is carried out by adjusting the initial phase andamplitude of the input sine tone such that at a given control point, the primary and secondary waves
can cancel each other completely.
Five control points illustrated in Figure 4(f) are simulated separately. Given the condition that thecontrol point is at the center and the primary noise source is placed on the right, the noise reduction
distributions of different secondary sources are shown in Figures 4(a) -(e). When linear secondary
sources are used, the quiet zone is a straight line, of which the width is proportional to the wavelength.
The quiet zone is curved and has a shorter length due to the PALs narrow directivities. However, when
the length-limited PAL is adopted, the quiet zone becomes longer, which implies that the beamwidthof the length-limited PAL is broader than the conventional PALs at the distance of the control point.
This can easily be validated in Figure 3(c).

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(a) 2 cm loudspeaker(b) 10 cm loudspeaker(c) PAL using a 40 kHz carrier(d) PAL using a 90 kHz carrier(e) Length-limited PAL(f) Overall layout of control points

Figure 4 – Noise reduction distributions when the control point is set at the center and the primarynoise source is placed on the right

3. ANALYSIS OF RESULTS
To summarize the results, two measures are considered. Firstly, the grids with noise reductions
above 3dB, 10 dB, and 20 dB are counted as percentages of the total number of grids. This measureindicates clearly the size of the quiet zone. Secondly, the averaged sound pressure level of the primarynoise in the whole simulation space is calculated. The change in the averaged sound pressure level
after the introduction of the secondary source is recorded. This measure explains whether the averagenoise level has been increased noticeably as a result of the spillover problem.
Figures 5 and 6 present the simulation results when the primary noise source is placed on the rightand on the top, respectively. In Figures 5(a) and 6(a), the number of grids where the noise reduction
is above 10 dB is likely to be independent from the secondary sources. For noise reduction above 20dB, using the linear secondary sources is more advantageous than using the nonlinear secondary58

sources. However, using the conventional PALs result in more grids with noise reduction above 3 dB.
This probably explains the previously reported observation that the quiet zone created by the PAL isperceived to be broader.
30(a) Grids with reduced noise levels

Percentage (%)

2520151053 dB
10 dB
20 dB0CenterLevel Change (dB)

8Top

BottomLeft

Right(b) Changes of the averaged sound pressure levels
Length-limited PAL
PAL using a 90 kHz carrier
PAL using a 40 kHz carrier
10 cm loudspeaker
2 cm loudspeaker

6420CenterTop

Bottom

Left

Right

Figure 5 – Simulation results when the primary noise source is placed on the right30(a) Grids with reduced noise levels

Percentage (%)

2520151053 dB
10 dB
20 dB0Center

Level Change (dB)

8Top

BottomLeft

Right(b) Changes of the averaged sound pressure levels
Length-limited PAL
PAL using a 90 kHz carrier
PAL using a 40 kHz carrier
10 cm loudspeaker
2 cm loudspeaker

6420CenterTopBottomLeftRightFigure 6 – Simulation results when the primary noise source is placed on the top
Moreover, the simulation space is relatively small as compared to practical situations. Using any
type of secondary source increases the averaged sound pressure level, but most of the increments areless than 3 dB. Figures 5(b) and 6(b) shows that the nonlinear secondary sources demonstrate themerit of less increments as compared to the linear secondary sources. When the control point is set on59

the right half plane, using the length-limited PAL is an exception. It results in a significant incrementin the averaged sound pressure level after noise cancellation. This is because the shortened length ofthe difference frequency beam cannot reach the control point as shown in Figure 3(c). On the other
hand, when the control point is on the left within the beam of the length-limited PAL, it achieves thesmallest spillover.

4. CONCLUSIONSA preliminary numerical study of local ANC has been conducted with different types of secondary
sources, including conventional loudspeakers, PALs and the length-limited PAL. Using the PALs canresult in less spillover as compared to the linear loudspeakers. It has been proved that when the control
point is within the beam of the length-limited PAL, the spillover problem can be further resolved.
However, there has been no observation that clearly supports the enlargement of the quiet zone byusing PALs in ANC.

ACKNOWLEDGEMENTS
This work is jointly supported by the Sichuan Science and Technology Program (Project No.
2019YJ0182) and National Science Foundation of China (Grant No. 61701090).

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