# Calculation of Noise Barrier Insertion Loss Based on Varied Vehicle Frequencies

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## Abstract

**:**

## 1. Introduction

## 2. Methods

#### 2.1. Measurement Method of Vehicle Noise Spectrum Data

#### 2.2. Noise Spectra of Different Vehicle Types and Speeds

- For a light vehicle, the noise energy is concentrated in the range of 500–2500 Hz, with peak frequency at approximately 1250 Hz. For a middle vehicle, the noise energy is concentrated in the range of 315–2500 Hz, with peak frequency at approximately 1600 Hz. For a heavy vehicle, the noise energy is concentrated in the range of 315–2500 Hz, with peak frequency at approximately 500 Hz.
- Speed will affect the SPL of a vehicle and the frequency characteristics of a vehicle. Noise spectra exhibit a trend of concentrating as the speed increase. Take the light vehicle case as an example, the noise energy percentage at the primary frequency range of 1000 Hz to 2500 Hz increases with speed, whereas the percentage of insignificant frequencies, such as low and medium-low frequencies, decrease with speeds. In addition, the main frequencies increase as the speed grows, especially for a light vehicle.
- The noise frequencies of the heavy vehicles are mainly medium-low frequency and medium-high frequency, which is quite different from the noise frequencies of light and middle vehicles, as their frequencies are mainly medium-high frequency.
- The emission noise of a vehicle can be divided into engine noise and tire/asphalt noise. Most of the light vehicles have gasoline engines. The contribution of engine noise is far less than the tire/asphalt noise. The proportion of diesel engines is high when for middle vehicles and heavy vehicles. The noise caused by diesel engine represents a large proportion, leading to a bi-modal trend in the noise spectra, which is in agreement with the rules presented by previous studies [34,35].

#### 2.3. The Calculation Method of Insertion Loss

- (1)
- Seven path length differences from 0.01 m to 10 m were preset first: 0.01 m, 0.1 m, 0.5 m, 1 m, 2.5 m, 5 m, 10 m;
- (2)
- The data were collected at the noise measurement site without the noise reduction effect of the barrier, and contained the 1/3rd-octave-band SPL ${L}_{i}$ and the total SPL L, where i is the sequence number of the 1/3rd-octave-band center frequency;
- (3)
- Through the diffraction formula, the diffraction $\Delta {L}_{di}$ of every 1/3rd-octave-band center frequency could be calculated as follows (Equation (4)):$$\Delta {L}_{di}=20\mathrm{lg}\frac{\sqrt{2\pi N}}{\mathrm{tanh}\sqrt{2\pi N}}+5\mathrm{dB},N=\frac{\delta \xb7f}{170}$$
- (4)
- For a certain path length difference, the total SPL ${L}^{\prime}$ with the reduction effect of noise barrier can be calculated as (Equations (5) and (6))$${{L}_{i}}^{\prime}={L}_{i}-\Delta {L}_{di}$$$${L}^{\prime}=10\mathrm{lg}({\displaystyle \sum _{i}{10}^{{{L}_{i}}^{\prime}/10}})$$
- (5)
- The following equation is used to yield the total diffraction $\Delta {L}_{d}$(Equation (7)):$$\Delta {L}_{d}=L-{L}^{\prime}$$
- (6)
- After calculating the total diffraction $\Delta {L}_{d}({\delta}_{j})$ and the 1/3rd-octave-band diffraction $\Delta {L}_{di}({\delta}_{j})$ with seven preset path length differences, the mean deviation $\Delta {d}_{i}$ between $\Delta {L}_{d}({\delta}_{j})$ and $\Delta {L}_{di}({\delta}_{j})$ can be obtained (Equation (8)).$$\Delta {d}_{i}=\frac{1}{7}{\displaystyle \sum _{j=1}^{7}\left|\Delta {L}_{d}({\delta}_{j})-\Delta {L}_{di}({\delta}_{j})\right|}$$

## 3. Experimental Verification

## 4. Effects of a Road Noise Barrier with Different Flow States

_{1}, R

_{2}, and R

_{3}) are chosen to analyze the effect of a road noise barrier with different type constituents and flow speed; all the receivers are sheltered by the barrier. The insertion losses of all receivers are calculated with different flow speed and the proportion of heavy vehicles. For each point, the SPL is calculated. The insertion loss of barrier can be defined as (Equation (12))

_{D}= SPL

_{0}−SPL

_{b}

_{0}is the SPL at the receiver when the barrier is absent and SPL

_{b}is the SPL at the same receiver when the barrier is present.

#### 4.1. Effect of Vehicle Type

_{D}presents a distinct pattern regarding points R

_{1}, R

_{2}, and R

_{3}, and the insertion loss at all of the receivers have relationships with the proportion of heavy vehicles. For point 1, L

_{D}and heavy vehicles a (%) follow the linear relationship of L

_{D}= −0.0293a + 24.661, i.e., 10 percent of heavy vehicles can cause a 0.29 dB decline on insertion loss in this scene. The results show that the SPL behind a barrier of a heavy vehicle flow is approximately 2.3 dB higher than that a light vehicle flow with the same source emission intensity. The same rule is also applicable to the overall shadow area. The heavy vehicles have more acoustical constituents at low frequencies compared to light vehicles, which are more significantly shaded by barriers. The insertion loss of heavy vehicle flow is the highest, followed by the insertion loss of mixed traffic flow, and the insertion loss of light vehicle flow is the lowest; this result indicates that the lower-frequency sound can bypass the barrier more easily. Thus, flow control of heavy vehicles whose sound is concentrated in low frequencies is an effective measure to improve the acoustic environment near roadways.

#### 4.2. Effect of Flow Speed

_{D}values, the analysis is as follows:

- The insertion losses of barrier increase with the flow speeds grow at all chosen points, regardless of the composition of vehicle types. For example, when the speed is below 40 km/h, the insertion loss of light vehicle flow at R
_{1}is approximately 23.7 dB, and the insertion loss increases non-linearly as the speed increases. At the speed of 90 km/h, the L_{D}value reached approximately 26.3 dB. - Figure 8 clearly shows that the noise barrier has sound-shading effects in all situations. The trend of increase of insertion loss with speed is observed, and the trend is considerably more obvious for light vehicle flow, middle traffic flow, and mixed traffic flow compared to heavy vehicle flow. The added L
_{D}value at R_{1}of a 30–90 km/h speed range of light vehicle flow, middle traffic flow, and mixed traffic flow is 2.65 dB, 1.73 dB, and 2.33 dB, respectively. However, the added insertion loss value of the same speed range of heavy vehicle flow is only 0.36 dB, which is considerably smaller. The data at R_{2}and R_{3}present the same rule because the main acoustics of light vehicle and middle vehicle are shifted to higher frequencies, whereas the main acoustics of heavy vehicle are slightly changed in frequency. - From the values, the SPL behind a barrier of a common mixed traffic flow with high speed is approximately 2 dB lower than the level with a low speed with the same source emission intensity. For a heavy vehicle flow, the sound pressure levels behind a barrier are little different with high or low flow speed.

## 5. Conclusions

## Acknowledgments

## Author Contributions

## Conflicts of Interest

## References

- Dehrashid, S.S.A.; Nassiri, P. Traffic noise assessment in the main roads of Sanandaj, Iran. J. Low Freq. Noise Vib. Act. Control
**2015**, 34, 39–48. [Google Scholar] [CrossRef] - Garacia, J.S.; Solano, J.J.P.; Serrano, M.C.; Camba, E.A.N.; Castel, S.F.; Asensi, A.S.; Suay, F.M. Spatial statistical analysis of urban noise data from a WASN gathered by an IoT system: Application to a small city. Appl. Sci. Basel
**2016**, 6, 380. [Google Scholar] [CrossRef] - Morel, J.; Marquisfavre, C.; Dubois, D.; Pierrette, M. Road traffic in urban areas: A perceptual and cognitive typology of pass-by noises. Acta Acust. United Acust.
**2012**, 98, 166–178. [Google Scholar] [CrossRef] - Di, G.Q.; Liu, X.Y.; Lin, Q.L.; Zheng, Y.; He, L.J. The relationship between urban combined traffic noise and annoyance: An investigation in Dalian, north of China. Sci. Total Environ.
**2012**, 432, 189–194. [Google Scholar] [CrossRef] [PubMed] - Roswall, N.; Raaschou-Nielsen, O.; Ketzel, M.; Overvad, K.; Halkjær, J.; Sørensen, M. Modeled traffic noise at the residence and colorectal cancer incidence: A cohort study. Cancer Cause Control
**2017**, 28, 745–753. [Google Scholar] [CrossRef] [PubMed] - Oiamo, T.H.; Luginaah, I.N.; Baxter, J. Cumulative effects of noise and odour annoyances on environmental and health related quality of life. Soc. Sci. Med.
**2015**, 146, 191–203. [Google Scholar] [CrossRef] [PubMed] - Monazzam, M.R.; Fard, S.M.B. Performance of passive and reactive profiled median barriers in traffic noise reduction. Appl. Phys. Eng.
**2011**, 12, 78–86. [Google Scholar] [CrossRef] - Reiter, P.; Wehr, R.; Ziegelwanger, H. Simulation and measurement of noise barrier sound-reflection properties. Appl. Acoust.
**2017**, 123, 133–142. [Google Scholar] [CrossRef] - Monazzam, M.R.; Lam, Y.W. Performance of profiled single noise barriers covered with quadratic residue diffusers. Appl. Acoust.
**2005**, 66, 709–730. [Google Scholar] [CrossRef] - Voropayev, S.I.; Ovenden, N.C.; Fernando, H.J.S.; Donovan, P.R. Finding optimal geometries for noise barrier tops using scaled experiments. J. Acoust. Soc. Am.
**2017**, 141, 722–736. [Google Scholar] [CrossRef] [PubMed] - Ishizuka, T.; Fujiwara, K. Performance of noise barriers with various edge shapes and acoustical conditions. Appl. Acoust.
**2004**, 65, 125–141. [Google Scholar] [CrossRef] - Arenas, J.P. Potential problems with environmental sound barriers when used in mitigating surface transportation noise. Sci. Total Environ.
**2008**, 405, 173–179. [Google Scholar] [CrossRef] [PubMed] - Zhao, W.C.; Chen, L.L.; Zheng, C.J.; Liu, C.; Chen, H.B. Design of absorbing material distribution for sound barrier using topology optimization. Struct. Multidiscip. Optim.
**2017**, 56, 315–329. [Google Scholar] [CrossRef] - Joynt, J. A Sustainable Approach to Environmental Noise Barrier Design. Ph.D. Thesis, University of Sheffield, Sheffield, UK, 2006. [Google Scholar]
- Kotzen, B.; English, C. Environmental Noise Barriers: A Guide to Their Acoustic and Visual Design; E & FN Spon-Routledge: London, UK, 1999. [Google Scholar]
- Sommerfeld, A. Mathematische theorie der diffraktion. Math. Ann.
**1896**, 47, 317–374. [Google Scholar] [CrossRef] - Wang, H.B.; Cai, M.; Zhong, S.Q.; Li, F. Sound field study of a building near a roadway via the boundary element method. J. Low Freq. Noise Vib. Act. Control
**2017**, in press. [Google Scholar] [CrossRef] - He, Z.C.; Li, G.Y.; Liu, G.R.; Cheng, A.G.; Li, E. Numerical investigation of ES-FEM with various mass redistribution for acoustic problems. Appl. Acoust.
**2015**, 89, 222–233. [Google Scholar] [CrossRef] - Hiraishi, M.; Tsutahara, M.; Leung, R.C.K. Numerical simulation of sound generation in a mixing layer by the finite difference lattice Boltzmann method. Comput. Math. Appl.
**2010**, 59, 2403–2410. [Google Scholar] [CrossRef] - Ma, D.Y.; Shen, H. Hankbook of Acoustics; SciPress: Beijing, China, 2004. [Google Scholar]
- Maekawa, Z. Noise reduction by screens. Appl. Acoust.
**1968**, 1, 157–173. [Google Scholar] [CrossRef] - Yamamoto, K.; Takagi, K. Expressions of Maekawa’s chart for computation. Appl. Acoust.
**1992**, 37, 75–82. [Google Scholar] [CrossRef] - Menounou, P. A correction to Maekawa’s curve for the insertion loss behind barriers. J. Acoust. Soc. Am.
**2001**, 110, 1828–1838. [Google Scholar] [CrossRef] [PubMed] - Kurze, U.J.; Anderson, G.S. Sound attenuation by barriers. Appl. Acoust.
**1971**, 4, 35–53. [Google Scholar] [CrossRef] - Cianfrini, C.; Corcione, M.; Fontana, L. Experimental verification of the acoustic performance of diffusive roadside noise barriers. Appl. Acoust.
**2007**, 68, 1357–1372. [Google Scholar] [CrossRef] - Li, K.M.; Wong, H.Y. A review of commonly used analytical and empirical formulae for predicting sound diffracted by a thin screen. Appl. Acoust.
**2005**, 66, 45–75. [Google Scholar] [CrossRef] - Anderson, G.S.; Menge, C.W.; Rossano, C.F.; Armstrong, R.E.; Ronning, S.A.; Fleming, G.G.; Lee, C.S.Y. FHWA traffic noise model, version 1.0: Introduction to its capacities and screen components. Wall J.
**1996**, 22, 14–17. [Google Scholar] - Shu, N.; Cohn, L.F.; Kim, T.K. Improving traffic-noise model insertion loss accuracy based on diffraction and reflection theories. J. Transp. Eng.
**2007**, 133, 281–287. [Google Scholar] [CrossRef] - Monazzam, M.R.; Nassiri, P. Contribution of quadratic residue diffusers to efficiency of tilted profile parallel highway noise barriers. Iran. J. Environ. Health Sci. Eng.
**2009**, 6, 271–284. [Google Scholar] - Grubeša, S.; Domitrović, H.; Jambrošić, K. Performance of traffic noise barriers with varying cross-section. PROMET-Traffic Transp.
**2011**, 23, 161–168. [Google Scholar] [CrossRef] - Huang, X.; Zou, H.; Qiu, X. A preliminary study on the performance of indoor active noise barriers based on 2D simulations. Build. Environ.
**2015**, 94, 891–899. [Google Scholar] [CrossRef] - Chen, S.M.; Wang, D.F.; Liang, J. Sound quality analysis and prediction of vehicle interior noise based on grey system theory. Fluct. Noise Lett.
**2012**, 11, 1250016. [Google Scholar] [CrossRef] - Ministry of Communications of the People’s Republic of China. Technical Specification for Construction of Asphalt Pavements; JTG F40-2004; Ministry of Communications of the People’s Republic of China: Beijing, China, 2005.
- Cai, M.; Zhong, S.Q.; Wang, H.B.; Chen, Y.X.; Zeng, W.X. Study of the traffic noise source intensity emission model and the frequency characteristics for a wet asphalt road. Appl. Acoust.
**2017**, 123, 55–63. [Google Scholar] [CrossRef] - Zhang, Y.F. Road Traffic Environmental Engineering; China Communications Press: Beijing, China, 2001. [Google Scholar]
- Ministry of Environmental Protection of the People’s Republic of China. Norm on Acoustical Design and Measurement of Noise Barriers; HJ/T 90-2004; Ministry of Environmental Protection of the People’s Republic of China: Beijing, China, 2004.

**Figure 2.**Noise energy percentage with the 1/3rd octave band spectrum frequencies at different speeds of three types of vehicles. (

**a**) light vehicles; (

**b**) middle vehicles; (

**c**) heavy vehicles.

**Figure 5.**Comparisons between 500 Hz frequency and the variety of equivalent frequencies for diffraction by barrier. (

**a**) light vehicle; (

**b**) middle vehicle; (

**c**) heavy vehicle.

**Figure 8.**Insertion loss of barrier with different flow speeds. (

**a**) Point R1; (

**b**) Point R2; (

**c**) Point R3.

Speed | Light Car | Middle Car | Heavy Car |
---|---|---|---|

[0, 40) km/h | 39 | 23 | 41 |

[40, 50) km/h | 186 | 48 | 80 |

[50, 60) km/h | 317 | 57 | 55 |

[60, 70) km/h | 222 | 38 | 36 |

[70, 80) km/h | 134 | ||

≥80 km/h | 75 |

Speed (km/h) | Light Car | Middle Car | Heavy Car | |||
---|---|---|---|---|---|---|

${\mathit{L}}_{1}$ | ${\mathit{L}}_{2}$ | ${\mathit{L}}_{1}$ | ${\mathit{L}}_{2}$ | ${\mathit{L}}_{1}$ | ${\mathit{L}}_{2}$ | |

[0, 40) | 75.21 | 46.31 | 84.26 | 52.11 | 83.91 | 54.38 |

[40, 50) | 80.69 | 48.98 | 83.85 | 52.42 | 80.12 | 48.84 |

[50, 60) | 80.09 | 49.03 | 86.59 | 53.76 | 85.95 | 53.39 |

[60, 70) | 82.17 | 50.14 | 85.53 | 53.99 | 86.68 | 54.17 |

[70, 80) | 82.74 | 50.65 | ||||

≥80 | 85.30 | 52.48 |

Vehicle Type | ${{\mathit{L}}_{1}}^{\prime}$ | ${{\mathit{L}}_{2}}^{\prime}$ | $\mathbf{\Delta}\mathit{L}$ |
---|---|---|---|

Light Car | 82.02 | 70.86 | 11.16 |

Middle Car | 84.13 | 73.10 | 11.03 |

Heavy Car | 84.02 | 72.89 | 11.13 |

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**MDPI and ACS Style**

Wang, H.; Luo, P.; Cai, M.
Calculation of Noise Barrier Insertion Loss Based on Varied Vehicle Frequencies. *Appl. Sci.* **2018**, *8*, 100.
https://doi.org/10.3390/app8010100

**AMA Style**

Wang H, Luo P, Cai M.
Calculation of Noise Barrier Insertion Loss Based on Varied Vehicle Frequencies. *Applied Sciences*. 2018; 8(1):100.
https://doi.org/10.3390/app8010100

**Chicago/Turabian Style**

Wang, Haibo, Peng Luo, and Ming Cai.
2018. "Calculation of Noise Barrier Insertion Loss Based on Varied Vehicle Frequencies" *Applied Sciences* 8, no. 1: 100.
https://doi.org/10.3390/app8010100