# Angle-Dependent Absorption of Sound on Porous Materials

^{1}

^{2}

^{3}

^{*}

## Abstract

**:**

## 1. Introduction

^{2}/year in 2017) with a biofiber-based solution, over 3000 tons of CO${}_{2}$ could be bound to buildings, which roughly equals the emissions from travelling by airplane for over 20 million kilometers [8].

## 2. Materials and Methods

#### 2.1. Studied Material Samples

#### 2.2. Experimental Setup

#### 2.3. Compensation of the Measurement Device Responses and Generation of Polar Responses

#### 2.4. Computation of the Angle-Dependent Absorption Coefficients

## 3. Results

## 4. Discussion

## 5. Conclusions

## Author Contributions

## Funding

## Acknowledgments

## Conflicts of Interest

## Abbreviations

MDPI | Multidisciplinary Digital Publishing Institute |

ISO | International Standard Organization |

CO${}_{2}$ | Carbon dioxide |

AES | Audio Engineering Society |

ITA | Institute of Technical Acoustics, Aachen, Germany |

O.d.s. | Overall depth of system |

## References

- D’Antonio, P.; Cox, T. Acoustic Absorbers and Diffusers: Theory, Design and Application; Taylor & Francis: Abingdon, UK, 2004. [Google Scholar]
- Venegas, R.; Umnova, O. Influence of sorption on sound propagation in granular activated carbon. J. Acoust. Soc. Am.
**2016**, 140, 755–766. [Google Scholar] [CrossRef] [PubMed][Green Version] - Berardi, U.; Iannace, G. Acoustic characterization of natural fibers for sound absorption applications. Build. Environ.
**2015**, 94, 840–852. [Google Scholar] [CrossRef] - Berardi, U.; Iannace, G. Predicting the sound absorption of natural materials: Best-fit inverse laws for the acoustic impedance and the propagation constant. Appl. Acoust.
**2017**, 115, 131–138. [Google Scholar] [CrossRef] - Jiménez, N.; Romero-García, V.; Pagneux, V.; Groby, J.P. Rainbow-trapping absorbers: Broadband, perfect and asymmetric sound absorption by subwavelength panels for transmission problems. Sci. Rep.
**2017**, 7, 13595. [Google Scholar] [CrossRef] [PubMed] - Tang, Y.; Ren, S.; Meng, H.; Xin, F.; Huang, L.; Chen, T.; Zhang, C.; Lu, T.J. Hybrid acoustic metamaterial as super absorber for broadband low-frequency sound. Sci. Rep.
**2017**, 7, 43340. [Google Scholar] [CrossRef] [PubMed][Green Version] - Arenas, J.P.; Asdrubali, F. Eco-materials with noise reduction properties. In Handbook of Ecomaterials; Martinez, L.M.T., Kharissova, O.V., Kharisov, B.I., Eds.; Springer International Publishing: Cham, Switzerland, 2019; pp. 3031–3056. [Google Scholar]
- Ciers, J.; Mandic, A.; Toth, L.D.; Op’t Veld, G. Carbon Footprint of Academic Air Travel: A Case Study in Switzerland. Sustainability
**2019**, 11, 80. [Google Scholar] [CrossRef][Green Version] - ISO 354. Acoustics—Measurements of Sound Absorption in a Reverberation Room; ISO: Geneva, Switzerland, 2003. [Google Scholar]
- ISO 10534-2. Acoustics—Determination of Sound Absorption Coefficient and Impedance in Impedance Tubes—Part 2: Transfer-Function Method; ISO: Geneva, Switzerland, 1998. [Google Scholar]
- Mommertz, E. Angle-dependent in-situ measurements of reflection coefficients using a subtraction technique. Appl. Acoust.
**1995**, 46, 251–263, Building Acoustics. [Google Scholar] [CrossRef] - Nocke, C. In-situ acoustic impedance measurement using a free-field transfer function method. Appl. Acoust.
**2000**, 59, 253–264. [Google Scholar] [CrossRef] - Garai, M. Measurement of the sound-absorption coefficient in situ: The reflection method using periodic pseudo-random sequences of maximum length. Appl. Acoust.
**1993**, 39, 119–139. [Google Scholar] [CrossRef] - Nolan, M. Estimation of angle-dependent absorption coefficients from spatially distributed in situ measurements. J. Acoust. Soc. Am.
**2020**, 147, EL119–EL124. [Google Scholar] [CrossRef] [PubMed][Green Version] - Karjalainen, M.; Tikander, M. Reducing Artefacts of In-Situ Surface Impedance Measurements. Available online: http://pcfarina.eng.unipr.it/Public/Standing-Wave/ica01.pdf (accessed on 15 October 2020).
- Brandão, E.; Lenzi, A.; Paul, S. A Review of the In Situ Impedance and Sound Absorption Measurement Techniques. Acta Acust. United Acust.
**2015**, 101, 443–463. [Google Scholar] [CrossRef] - Vorländer, M.; Mommertz, E. Definition and measurement of random-incidence scattering coefficients. Appl. Acoust.
**2000**, 60, 187–199. [Google Scholar] [CrossRef] - ISO 17497-1. Acoustics—Sound-Scattering Properties of Surfaces—Part 2: Measurement of the Random-Incidence Scattering Coefficient in a Reverberation Room; ISO: Geneva, Switzerland, 2004. [Google Scholar]
- D’Antonio, P.; Cox, T. AES information document for room acoustics and sound reinforcement systems-characterization and measurement of surface scattering uniformity. J. Audio Eng. Soc.
**2001**, 49, 149–165. [Google Scholar] - ISO 17497-2. Acoustics—Sound-Scattering Properties of Surfaces—Part 2: Measurement of the Directional Diffusion Coefficient in a Free Field; ISO: Geneva, Switzerland, 2012. [Google Scholar]
- Jahangiri, P.; Logawa, B.; Korehei, R.; Hodgson, M.; Martinez, D.M.; Olson, J.A. On acoustical properties of novel foam-formed cellulose-based material. Nord. Pulp Pap. Res. J.
**2016**, 31, 14–19. [Google Scholar] [CrossRef] - Kerekes, R.J.; Schell, C.J. Effects of fiber length and coarseness on pulp flocculation. Tappi J.—(USA)
**1995**, 78, 133–139. [Google Scholar] - Beghello, L.; Eklund, D. Some mechanisms that govern fiber flocculation. Nord. Pulp Pap. Res. J.
**1997**, 12, 119–123. [Google Scholar] [CrossRef] - Lappalainen, T.; Lehmonen, J. Determinations of bubble size distribution of foam-fibre mixture using circular hough transform. Nord. Pulp Pap. Res. J.
**2012**, 27, 930–939. [Google Scholar] [CrossRef] - Haimei, Z.; Ma, S.; Wu, Y. Building Materials in Civil Engineering; Elsevier: Amsterdam, The Netherlands, 2011; Volume 80, pp. 81–308. [Google Scholar]
- Berzborn, M.; Bomhardt, R.; Klein, J.; Richter, J.G.; Vorländer, M. The ITA-Toolbox: An open source MATLAB toolbox for acoustic measurements and signal processing. In Proceedings of the 43th Annual German Congress on Acoustics, Kiel, Germany, 6–9 March 2017; Volume 2017, pp. 6–9. [Google Scholar]
- Farina, A. Simultaneous measurement of impulse response and distortion with a swept-sine technique. In Audio Engineering Society Convention 108; Audio Engineering Society: New York, NY, USA, 2000. [Google Scholar]
- ISO 3382-1. Measurement of Room Acoustic Parameters—Part 1: Performance of Spaces; ISO: Geneva, Switzerland, 2009. [Google Scholar]
- Hald, J.; Song, W.; Haddad, K.; Jeong, C.H.; Richard, A. In-situ impedance and absorption coefficient measurements using a double-layer microphone array. Appl. Acoust.
**2019**, 143, 74–83. [Google Scholar] [CrossRef] - Datasheet of Perforated Panels Provided by Their Manufacturer Knauf Danoline. Available online: https://knaufdanoline.com/wp-content/uploads/Data_sheet_Solopanel_UK.pdf (accessed on 31 August 2020).
- Yamaguchi, M.; Nakagawa, H.; Mizuno, T. Sound absorption mechanism of porous asphalt pavement. J. Acoust. Soc. Jpn. (E)
**1999**, 20, 29–43. [Google Scholar] [CrossRef][Green Version] - Swift, M.; Bris, P.; Horoshenkov, K. Acoustic absorption in re-cycled rubber granulate. Appl. Acoust.
**1999**, 57, 203–212. [Google Scholar] [CrossRef]

**Figure 1.**(

**a**,

**b**) illustrates the cross-sectional porous structure of bioboard and glass-wool, for the impedance tube samples, and the samples used for the determination of incidence angle-dependent sound absorption coefficients. (

**c**–

**e**) show scanning electron microscopy images of dissolving hardwood, bleached softwood and glass fibers, respectively.

**Figure 2.**The applied measurement system (on the left). The loudspeaker can be moved on rails from 0${}^{\circ}$ to 85${}^{\circ}$ and there are 16 microphones at 5${}^{\circ}$ spacing, from 10${}^{\circ}$ to 85${}^{\circ}$. On the right, the measured materials are shown and the porous materials were mounted in a wooden frame, seen top right.

**Figure 3.**Dimensions and arrangement of the receiver array and the sound source in the measuring device.

**Figure 4.**The process to extract the reflection from the panel under test. On the left, responses measured for a gypsum panel; on the right, responses measured for a bioboard panel.

**Figure 5.**Incident and reflected sound energy from a specimen, ${I}_{\mathrm{i}}$ and ${I}_{\mathrm{r}}$, respectively.

**Figure 6.**One-third octave polar responses at selected center frequencies for four angles of sound incidence 30${}^{\circ}$, 45${}^{\circ}$, 60${}^{\circ}$ and 75${}^{\circ}$. The circles (starting from the x-axis) indicate the levels in decibels.

**Figure 7.**Sound absorption coefficients at one-third octave bands, measured for four angles of sound incidence 30${}^{\circ}$, 45${}^{\circ}$, 60${}^{\circ}$ and 75${}^{\circ}$.

**Figure 8.**Sound absorption coefficients at one-third octave bands, measured for four angles of sound incidence 30${}^{\circ}$, 45${}^{\circ}$, 60${}^{\circ}$ and 75${}^{\circ}$.

**Figure 9.**Normal sound incidence and diffuse field sound absorption coefficients measured with an impedance tube and in a reverberation room, respectively. The materials investigated are bioboard (blue lines) and 50-mm glass-wool (red lines). The thickness of the bioboard panels differ between 35 and 50 mm. The normal sound incidence sound absorption coefficients were measured with a large impedance tube for the frequency range 125–1000 Hz, and with a small impedance tube for the frequency range 1000–6000 Hz (note that 6000 Hz is the cut-off frequency of the small impedance tube).

**Table 1.**Investigated materials. The overall depth for all the structures was approximately 50 mm, except for the plain gypsum.

Material | Manufacturer | o.d.s. | Density | % of Perforation |
---|---|---|---|---|

Plain gypsum | Knauf | 13 mm | ||

Knauf | 13 mm + | Square 8 mm, 20% | ||

37 mm air-gap | ||||

Perforated gypsum | Knauf | 13 mm + | Square 8 mm, 20% | |

17 mm air-gap + | ||||

20 mm stone wool | ||||

Glass-wool | Ecophon | 50 mm | $\rho =$ 52 kg/m${}^{3}$ | |

Bioboard | Lumir | 47 mm | $\rho =$ 60 kg/m ${}^{3}$ |

**Table 2.**Physical properties of the wood fibers used in the production of the bioboard panels. The reported fiber length is the length-weighted average fiber length. Length and width of glass fibers are reported for comparison [25].

Fiber Type | Length (mm) | Width ($\mathsf{\mu}$m) | Curl (%) |
---|---|---|---|

$H{W}_{dissolving}$ | 0.73 | 16.32 | 17.7 |

$S{W}_{bleached}$ | 1.97 | 25.36 | 15.4 |

$Glassfiber$ | 50–150 | 12 |

**Table 3.**Background noise levels during the measurements. Measurements obtained using a sound analyser Norsonic Nor140.

Central Frequencies of the Octave Frequency Bands (Hz) | 125 | 250 | 500 | 1000 | 2000 | 4000 | 8000 |
---|---|---|---|---|---|---|---|

${L}_{\mathrm{eq}}$ (dB) | 43.2 | 38.6 | 36.3 | 30.8 | 23.4 | 15.6 | 14.4 |

${\mathit{h}}_{1}-{\mathit{h}}_{2}$ | ${\mathit{h}}_{3}$ |
---|---|

10${}^{\circ}$, 15${}^{\circ}$, 20${}^{\circ}$ | 15${}^{\circ}$ |

25${}^{\circ}$, 30${}^{\circ}$, 35${}^{\circ}$ | 30${}^{\circ}$ |

40${}^{\circ}$, 45${}^{\circ}$, 50${}^{\circ}$ | 45${}^{\circ}$ |

55${}^{\circ}$, 60${}^{\circ}$, 65${}^{\circ}$ | 60${}^{\circ}$ |

70${}^{\circ}$, 75${}^{\circ}$, 80${}^{\circ}$ | 75${}^{\circ}$ |

Publisher’s Note: MDPI stays neutral with regard to jurisdictional claims in published maps and institutional affiliations. |

© 2020 by the authors. Licensee MDPI, Basel, Switzerland. This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution (CC BY) license (http://creativecommons.org/licenses/by/4.0/).

## Share and Cite

**MDPI and ACS Style**

Cucharero, J.; Hänninen, T.; Lokki, T.
Angle-Dependent Absorption of Sound on Porous Materials. *Acoustics* **2020**, *2*, 753-765.
https://doi.org/10.3390/acoustics2040041

**AMA Style**

Cucharero J, Hänninen T, Lokki T.
Angle-Dependent Absorption of Sound on Porous Materials. *Acoustics*. 2020; 2(4):753-765.
https://doi.org/10.3390/acoustics2040041

**Chicago/Turabian Style**

Cucharero, Jose, Tuomas Hänninen, and Tapio Lokki.
2020. "Angle-Dependent Absorption of Sound on Porous Materials" *Acoustics* 2, no. 4: 753-765.
https://doi.org/10.3390/acoustics2040041