PROCEEDINGS of the
23rd International Congress on Acoustics
9 to 13 September 2019 in Aachen, Germany

Sound Absorption of Thin Resonators Including a Winding Neck
Extension in Surface Panel
Shinsuke NAKANISHI1
1

Hiroshima Institute of Technology, Japan

ABSTRACT
Acoustic resonant absorber like a perforated panel or a Helmholtz resonator can be tuned at a low frequency
by extending its neck or enlarging cavity volume. However, a total size of the resonators is often quite large
when the neck or the cavity is simply extended for tuning at a low frequency. Previous researchers havestudied Helmholtz resonator shortened in its size by subsided neck into back air cavity, and confirm that thisresonator is tuned at low frequency without a deep cavity. The author has studied effects of a winding built-inneck extension to sound absorption of perforated panels and Helmholtz resonators, which show same effects
as the subsided neck into back cavity. This study measures and discusses sound absorption of thin resonator
tuned at a low frequency. Test pieces have various neck extensions built in a surface panel and 15 mm total
thickness of resonators to propose as sound absorption tiles attaching on walls or partitions. Discussions inthis paper focus effects of opening size of the resonator, path length, patterns or number of turns of thewinding neck extension and cavity volume to the sound absorption of the thin resonator.
Keywords: Sound, Absorption, Resonator

1. INTRODUCTION
The previous studies have studied effects of sound absorption by a small size resonator tuning at a
low and middle frequency, and it is typical method to enlarge cavity volume or neck length of theresonator tuned at low frequency. These typical methods enlarge total size of resonators or soundabsorption structures. Small size of sound absorbers are often needed for turning a reverberation timeor reducing an environmental noise in small chamber room e.g. a meeting room, a practice room formusic and a cabin in air plane or ship.
To shorten the size of resonator, Iwase et al.[1] have studied the effects on acoustic resonance by
the subsiding changes of neck from original type Helmholtz resonator and by the adapting of extension
parts to opening hole of perforated panel. From their experimental research to make shortening size ofHelmholtz resonator and lowering resonant frequency of sound absorption of perforated panel, they
conclude that use of extension parts to the opening hole on the perforated plate is effective to lower the
resonance frequency simply. They have also obtained the same effects of extension parts with turnback shape in the cavity as with straight shape. And, Iwase et al.[2] have verified the high soundabsorption at low frequency by the method adding extension part behind opening holes. They could
also have the empiric model to calculate the acoustic impedance and the sound absorption coefficientfor their new type resonator.
As applications from the previous study by Iwase et al., the author[3] considered that the extension
parts are built in perforated panel with multi-turn back shape. Measurements of its sound absorption
coefficient and considerations on effects of the winding extension to the resonant sound absorption
show that the extension shifts its resonant peak to lower frequency without change of depth of air
cavity which affects total thickness of the sound resonator. The shift amount of the resonant frequency
is quite close between the straight extension and the winding extension when its section area is 3 mmside of square and 2.4 mm side of square, although the shift amount increases when the section area is
1.8 mm side of square as the winding extension including twice of rectangle corners to same length of
the above cases.
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s.nakanishi.9a@cc.it-hiroshima.ac.jp

Moreover, the author[4] discussed sound absorption of the resonator included the various winding
neck extension built in a surface panel. A winding neck extension built in upper plate of the Helmholtz
resonator is useful method to tune it at lower resonant frequency. Structure of winding extension tube
is generally made with any turn-backed tube, although this study show that the resonant does notappear for 1.8 mm side of square opening with 40 mm of extension tube. And, This study indicated that
8 turn back of 80 mm of extension tube shifts the resonance to 23 % higher frequency than designed
resonance frequency, because a virtual path of air flow in the tube is narrower than the physical crosssection[5]. It seemed to be caused by a vortex at inner wall of 180-degree turn due to turbulent flow
separation in a rectangular tube.
This study measures and discusses sound absorption of thin resonator tuned at a low frequency. Test
single Helmholtz resonators have various neck extensions built in a surface panel and 10mm or 15 mm
total thickness of resonators to propose as sound absorption tiles attaching on walls or partitions.
Discussions in this paper focus effects of opening size of the resonator, path length, patterns or numberof turns of the winding neck extension and cavity volume to the sound absorption of the thin resonator.

2. MEASUREMENT
2.1 Procedure
The sound absorption coefficient of test Helmholtz resonator including a winding neck extension ina surface panel is obtained by surface normal impedance 𝑍",$% at the opening hole, which is measured
by in-situ measurement method[6]. Figure 1 and Figure 2 indicate procedure of measuring theirsurface normal impedance in workshop of Hiroshima International University. The test Helmholtz
resonator is built in a box of 120 mm side of upper square surface and 60 mm height which is placed on
the rigid floor.
Two microphones are placed at the opening hole of test Helmholtz resonator for measuringtransmission function 𝐻'' between them, is needed to calculate normal surface impedance by in-situ
measurement method. Incoherent pink noise from five loudspeakers in the workshop makes randomsound incidence to the surface of test Helmholtz resonator.
The normal surface impedance of test perforated panel is obtained by following equation:
𝑍",$% = 𝜌𝑐𝐻'' +1 − 𝑒 /01(345) 7 − 𝑒 013 +1 − 𝑒 /015 7
𝐻'' (1 + 𝑒 /01(345) ) − 𝑒 013 (1 + 𝑒 /015 )(1)Here, d is distance between the surface of test piece and lower microphone, l is 14 mm distance
between centers of two microphones, r is air density, c is sound speed in the air, k is wave number
and j is the imaginary unit.

Figure 1 – Procedure of in-situ measurement method for measuring normal surface impedance at an
opening hole of test Helmholtz resonator.

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Figure 2 – Positions of the test Helmholtz resonator on a floor in the workshop and two microphones
at an opening hole of the resonator.
2.2 Structures of test Helmholtz resonators
Figure 3 shows a test Helmholtz resonator built in the box like double shells filled clay between
them. The clay is used to fix vibration of shells by its large mass and large viscosity. Each part ismodeled by Google SketchUp and is made by 3D printing (MakerBot, Replicator2) with polylactic
acid plastics. The resonator has a square opening hole, a winding neck extension tube with a squaresection and a rectangular cavity behind it. Each resonator is designed to be tuned at 200 Hz by thefollowing formula:𝑓;<= =𝑐𝑆@
2𝜋 𝑉(𝑙 + 0.8 𝑑H )

[Hz]

(2)

Here, c is sound speed in the air [m/s], S is area of opening hole [m2 ], V is volume of cavity [m3 ], l is
length of neck and 𝑑H is diameter of equivalent circle with same area of the square opening hole.
Test Helmholtz resonators have 10 mm or 15 mm of total thickness from a surface plate to abottom of the cavity. A extension tube attached at opening hole has 80 mm length for all test
Helmholtz resonators. A side length of its square opening holes has 2.4 mm, 3.0 mm and 3.6 mm,
and numbers of turn backs of extension tube are 1 to 13 turn backs, 1 to 10 turn backs and 1 to 8 turnbacks respectively. And, a resonant frequency of these resonators is tuned 100 Hz or 200 Hz. Detailspecifications are indicated in Table 1.

Figure 3 – A cross section of a test Helmholtz
resonator built in a box of 120 mm side of uppersquare surface and 60 mm height filled clay
between them.

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Figure 4 – Examples of the Helmholtz resonator
having 3 turn backs of winding extension tube
built in the upper plate.

Table 1 – Specifications of test Helmholtz resonators with 80 mm length of neck built in surface plate.
Cavity volume(mm3 )(section area × depth)

Number of turn backs

15 mm

2.4
3.0
3.6

21.22 × 10.2
26.42 × 10.2
31.62 × 10.2

1 to 13
1 to 10
1 to 8

10 mm

2.4
3.0
3.6

28.32 × 5.2
35.32 × 5.2
42.22 × 5.2

1 to 13
1 to 10
1 to 8

2.4
3.0
3.6

42.42 × 10.2
52.92 × 10.2
63.22 × 10.2

1 to 13
1 to 10
1 to 8

Total thickness (mm)Square hole size (mm)(1) Resonant frequency is 200 Hz.

(2) Resonant frequency is 100 Hz.
15 mm

3. RESULTS AND DISCUSSION
3.1 Frequency characteristics of absorption coefficientThis section focuses sound absorption of thin Helmholtz resonator and discusses effects of turnbacks in the winding extension tube to the sound absorption.
All test resonators with a 2.4 mm squared opening hole have no resonant peak around 200 Hz or 100
Hz designed by Eq. 2. As mentioned previous study[4], it is well known that resonance of theresonator becomes weak and small value due to a large pressure loss ΔP of a straight cylindricalduct is inversely proportional to its diameter as following formula:
ΔP = λ𝐿 𝜌 𝑣/
𝑑 2

[Pa]

(3)

Here, λ is a friction factor of the duct, 𝐿 [m] is its length, 𝑑 [m] is its diameter, 𝜌 [kg/m3 ] isthe density of the air and 𝑣 [m/s] is speed of air flow in the duct. When the pressure loss enlarges
with narrow tube, the pressure at a bottom of extension tube attached the cavity becomes smallpressure from the opening hole and can not compress a volume of the cavity as air spring consistinga resonator with mass of air in the neck. As the results, a significant peak of the absorption
coefficient of the resonator with 2.4 mm squared opening hole.
Figures 5,6 and 7 indicate three examples of absorption coefficient of test Helmholtz resonatorswith 3.0 mm or 3.6 mm squared opening holes, which have a peak around 200 Hz or 100 Hz as aresonant frequency designed by Eq. 2. In the figures, black solid line has a median peak value aroundthe resonant frequency of the resonator with various numbers of turn back in the winding extension
tube. Red solid line and blue solid line have a maximum and a minimum peak value respectively, andshow a variation range of effects by turn back of the winding extension tube.
These figures show that a significant peak around 200 Hz or 100 Hz designed by Eq. 2 is found inabsorption coefficient of each test resonator. This study obtained a unit resonator consisting thinnersound absorption structure even with 10 mm of total thickness, in compared with 19.8 mm of total
thickness of Helmholtz resonators in the previous study[4]. This study also suggests that thin plane
resonant sound absorber with 15 mm of total thickness tuned at 100 Hz can be assembled many small
unit resonators. Here, the resonator with 3.6 mm squared opening hole tuned at 100 Hz has a large peakvalue of absorption coefficient.

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(1) 3.0 mm squared of opening hole(2) 3.6 mm squared of opening hole

Figure 5 – Three examples of absorption coefficient of the resonator. Resonant frequency is tuned at
200 Hz and the total thickness 15 mm. Black solid line indicates median peak value, red solid line
indicates maximum peak value and blue line indicates minimum peak value(1) 3.0 mm squared of opening hole(2) 3.6 mm squared of opening hole

Figure 6 – Three examples of absorption coefficient of the resonator. Resonant frequency is tuned at
200 Hz and the total thickness 10 mm. Black solid line indicates median peak value, red solid line
indicates maximum peak value and blue line indicates minimum peak value(1) 3.0 mm squared of opening hole(2) 3.6 mm squared of opening hole

Figure 7 – Three examples of absorption coefficient of the resonator. Resonant frequency is tuned at
100 Hz and the total thickness 15 mm. Black solid line indicates median peak value, red solid line
indicates maximum peak value and blue line indicates minimum peak value

3.2 Peak frequency and peak value of absorption coefficientThis section focuses peak frequency and peak value of absorption coefficient of the test Helmholtz
resonators with various number of turn back of neck extension tube.
Figures 8 and 9 indicate peak frequency and peak value of absorption coefficient of the resonators
tuned at 200 Hz. Almost of all resonators have a peak frequency at around 209 Hz shifted toward2324

higher frequency than a designed resonant frequency of 200 Hz with its difference of 9 Hz (4.5 %).
This shift difference seems to be independent from number of turn back of neck extension tube andbetween 3.0 mm and 3.6 mm squared opening hole. Previous study[4] shows that peak frequency shifts
toward higher as increasing numbers of turn backs of neck extension tube with 3.6 mm squared
opening hole up to 246 Hz with 8 turn backs.
Peak values of absorption coefficient vary 0.3 to 0.6 in case of 15 mm total thickness of resonators
tuned at 200 Hz and seem to be independent from number of turn backs of neck extension tube. And,the peak values for the resonators with 3.6 mm squared opening hole are slightly larger than 3.0 mm
squared opening holes in case of 1 to 6 turn backs of neck extension tubes. Moreover, peak values ofabsorption coefficient vary 0.3 to 0.7 in case of 10 mm total thickness of resonators tuned at 200 Hz.
Similarly, peak values for the resonators with 3.6 mm squared hole are larger than 3.0 mm squared
opening hole in case of 1 to 5 turn backs. Previous study[4] shows that large peak values are obtainedin case of 3, 4 and 5 turn backs and that their values of absorption coefficient are around 0.6. In
previous study and this study, test Helmholtz resonators ware made by 3D printing (MakerBot,
Replicator2) with polylactic acid plastics. Because this 3D printing is based on Fused deposition
modeling, inner wall in neck extension tube fluctuates and varies its friction loss.
Figure 10 indicates peak frequency and peak value of absorption coefficient of the resonators tuned
at 100 Hz. Peak frequencies are around 100 Hz except for the resonator with 3.6 mm squared opening
hole and 8 turn backs. Although the resonators with 3.0 mm squared opening hole shows that peakvalue varies 0.3 to 0.5, the resonators with 3.6 mm squared opening hole shows that peak values reduce
as increasing number of turn backs of the extension tube.

(1) Peak frequency of absorption coefficient(2) Peak value of absorption coefficient

Figure 8 – Effects of number of turn backs of winding neck extensions to peak frequency and peakvalue of absorption coefficient around resonant frequency designed for test Helmholtz resonators.
Resonant frequency is 200 Hz and total thickness is 15 mm. Open circles indicate the resonator with
3.6 mm squared hole and black circles indicate the resonator with 3.0 mm squared hole.

(1) Peak frequency of absorption coefficient(2) Peak value of absorption coefficient

Figure 9 – Effects of number of turn backs of winding neck extensions to peak frequency and peakvalue of absorption coefficient around resonant frequency designed for test Helmholtz resonators.
Resonant frequency is 200 Hz and total thickness is 10 mm. Open circles indicate the resonator with
3.6 mm squared hole and black circles indicate the resonator with 3.0 mm squared hole.

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(1) Peak frequency of absorption coefficient(2) Peak value of absorption coefficient

Figure 10 – Effects of number of turn backs of winding neck extensions to peak frequency and peakvalue of absorption coefficient around resonant frequency designed for test Helmholtz resonators.
Resonant frequency is 100 Hz and total thickness is 15 mm. Open circles indicate the resonator with
3.6 mm squared hole and black circles indicate the resonator with 3.0 mm squared hole.

4. CONCLUSIONSThis study measured and discussed sound absorption of thin resonator tuned at a low frequency.
Test single Helmholtz resonators have various neck extensions built in a surface panel and 10mm or 15
mm total thickness of resonators to propose as sound absorption tiles attaching on walls or partitions.
Discussions in this paper focused effects of opening size of the resonator, path length, patterns or
number of turns of the winding neck extension and cavity volume to the sound absorption of the thinresonator.
The author suggests following conclusions.
(1) A winding neck extension tube built in surface plate can give a thin resonant sound absorber,
which will be used as tiles set on a wall or a partition to control the reverberant time or noise
reduction in small camber room.
(2) This study confirmed that peak frequency equally shifts toward higher than the designed resonant
frequency for the resonators tuned at 200 Hz as shown in previous study[4], although previous
study shows peak frequency becomes higher as increasing number of turn backs.
(3) The resonators tuned at 100 Hz are available for producing thin sound absorber at low frequency.
Future study will discuss sound absorbing tile at low frequency by assembled many resonator
unit.

REFERENCES
1. Teruo Iwase, Keiko Shirahata, Akiko Igarashi, Satoshi Sugie, Yasuaki Okada, "Shortening Helmholtz
resonator by subsided neck and application to perforated plate structure for low frequency soundresonance," Proceedings in DVD-ROM on internoise2012 (2012, New York, NY), 12p (2012).
2. Teruo Iwase, Satoshi Sugie, Masayuki Abe, Hiroyasu Kurono, Shinya Nishimura, Yasuaki Okada andKoichi Yoshihisa, "Modeling and verification of perforated plate structure for high sound absorption at
low frequency with extending parts behind holes into shallow air space," Proceedings in DVD-ROM on
internoise2015 (2015, San Francisco, CA), 12p (2015).
3. Shinsuke Nakansihi, "A pilot study of acoustic absorption by a perforated panel with bending tube
extension built in the panel," Proceedings in DVD-ROM on internoise2015 (2015, San Francisco, CA),
10p (2015).
4. Shinsuke Nakanishi, "Sound absorption of Helmholtz resonator included a winding built-in neckextension," Proceedings of internoise2016 (2016, Hamburg, Germany), 8p (2016).
5. Hitoshi Sugiyama, Tatsuya Tanaka and Hideaki Mukai, "Numerical analysis of turbulent flow separation
in a rectangular duct with a sharp 180‐degree turn by algebraic Reynolds stress model," International
Journal for Numerical Methods in Fluids, 56(12), 2207–2228
6. Yasuo Takahashi, Toru Otsuru and Reiji Tomiku, "In situ measurements of surface impedance andabsorption coefficients of porous materials using two microphones and ambient noise," Applied
Acoustics, 66, 845-865 (2005)

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