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An efficient method to calculate sound diffraction over obstacles

Accurate and efficient calculations of diffraction over rigid obstacles are very useful for sound propagating over city canyons and for situations where fast evaluations are required, such as for virtual reality sound effects or for the sound effect in video games. Uniform diffraction theory offers very accurate solutions for sound diffraction over obstacles. However, these solutions depend on very complicated input parameters and usually take more CPU time than engineering approximations. In this paper, a serial simplified diffraction function to approximate single, double and multiple diffractions is presented. The formulation of these functions is based on the simplification of Fresnel integral and their accuracies depend on the relative locations among the source, obstacle and receiver. Compared with the non-simplified diffraction function, most of the receiver positions can reach an acceptable accuracy except the positions close to the boundary line where 3 dB error is expected.

Geometry studied

The cases studies include single, double, and two multiple diffraction scenarios as shown below.

Various geometries studied for modelling the diffraction of sound

Insertion loss based on the simplified method

The equations for single, double and multiple diffractions are shown below.

Single, double, and multiple diffraction


The simplified method is validated by comparing results with the Pierce solution.  The deviated errors between the two methods for the above four cases are shown below:

  • Single diffraction: case (a)
Validation of single diffraction case
  • Double diffraction: case (b)
Validation of double diffraction case
  • Multiple diffraction (level difference): case (c) and (d)
Validation of multiple diffraction case

Further reading

The full paper is available to download below.

EURONOISE2015 – An efficient method to calculate sound diffraction over rigid obstacles

Posted in: Environmental noise modelling

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