![diffraction of sound equation diffraction of sound equation](https://www.spiedigitallibrary.org/ContentImages/Journals/OPEGAR/58/8/087105/FigureImages/OE_58_8_087105_f005.png)
The full paper is available to download below. Multiple diffraction (level difference): case (c) and (d).The deviated errors between the two methods for the above four cases are shown below:
![diffraction of sound equation diffraction of sound equation](https://i.ebayimg.com/images/g/kbYAAOSwqtRl1ofZ/s-l960.jpg)
The simplified method is validated by comparing results with the Pierce solution. THE SOUND PRESSURE FIELD The sound pressure field 0 (M) will be primarily described in terms of the Helmholtz equation, in two or three dimensions, together with appropriate boundary conditions. The equations for single, d ouble and multiple diffractions are shown below. Insertion loss based on the simplified method The cases studies include single, double, and two multiple diffraction scenarios as shown below. 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. 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.
![diffraction of sound equation diffraction of sound equation](https://i.pinimg.com/originals/c1/2f/4b/c12f4ba38148378536649d4e7d342e1f.gif)
In this paper, a serial simplified diffraction function to approximate single, double and multiple diffractions is presented. However, these solutions depend on very complicated input parameters and usually take more CPU time than engineering approximations. Uniform diffraction theory offers very accurate solutions for sound diffraction over obstacles. Here, the outer surface is assumed to be lined with acoustically absorbing material which makes the problem more complicated. The WienerHopf technique is engaged to obtain total diffracted field. 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. Diffraction of sound waves from a circular cylindrical cavity is presented rigorously.