# Angle-Dependent Absorption of Sound on Porous Materials

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## 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 |

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**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${}^{\circ}$ |

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## 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