Diffraction Sandbox - Version 0

Acoustic diffraction is sometimes discussed with a sense of mystery.

This is, in part, because it is defined negatively: It is the part of the solution to the linear wave equation which remains when the specular approximation is subtracted from it.

There are several ways of conceptualizing acoustic diffraction, and many models,
each approach being best suited to a particular application.

This document is still developing...If does not quench your curiosity, additional resources are at the bottom.

Here, we implement the solution derived in Medwin's 1982 paper.

This paper was significant because it was the first time a transient solution for diffraction around the edge of a wedge was derived. All prior solutions assumed the source was continuous, or cyclically repeating eternally. This distinction makes the solution appropriate for use in calculating impulse responses applied to impulsive sources.

Stated another way, this theory predicts the waveform that would propagate around a wedge shaped barrier, if the direct sound, and the sound reflected from the wedge faces (predicted by specular theory) was removed.

The tip of the wedge in the image below is the origin. The edge of the wedge, is the z axis. The edge is finite, and extends from z1= meters to z2= meters from the origin.

The solid angle of the wedge, 360° - θw = °, or radians

Source Position:
In Cartesian Coordinates (x, y, z) = [ , , ] meters
In Cylindrical Coordiantes (r, θ, z) =[ meters, radians, meters]

Receiver Position:
In Cartesian Coordinates (x, y, z) = [ , , ] meters
In Cylindrical Coordiantes (r, θ, z) =[ meters, radians, meters]

To the left, is a view of a wedge shaped barrier, looking along the axis. You can adjust the source and receiver position in the X-Y plane by dragging them. To adjust their location along the z axis, there are drag the position numbers at the top. The diffracting wedge is finite along the z-axis, you can alter the endpoints above as well.

The impulse to the right is first order edge diffraction, calculated using the equations below, and reproduced from [2]. The waveform shown is one second in duration.

Which is shorthand for the sum of the following terms:

Well, that's lovely... but what's the point ?

  • This theory can be used to predict the amplitude of noise diffracted around barriers.

  • The theory above can be applied to EVERY wedge in a geometry that sound is incident upon, the superposition of all the solutions would give the impulse response of the diffracted field.

Heuristic Observations

  • The closer the receiver to the "shadow boundary" that is, the line demarkating the transition between where the specular field is present and is not present, exhibits the largets diffracted contribution.

  • The longer the edge of the wedge, the longer the diffracted impulse response in time, this indicates more diffracted low frequency content.

  • Both the direct and reflected waves have "shadow boundaries" because the wedge occludes some of the specular field, and the reflected specular field comes from a finite reflector

  • The diffracted field changes signs as it crosses each "shadow boundary".

Resources Consulted

[1] The framework for this page was shamelessly stolen from http://worrydream.com/Tangle/

[2] Medwin, H., Childs, E., & Jebsen, G. M. (1982). Impulse studies of double diffraction: A discrete Huygens interpretation. Journal of the Acoustical Society of America, 72(September), 1005–1013.

[3] JavaScript: The Good Parts by Douglas Crockford. Copyright 2008 Yahoo! Inc., 978-0-596-51774-8

[4] Hart, C. R. (2014). On a combined adaptive tetrahedral tracing and edge diffraction model. University of Nebraska - Lincoln. Retrieved from http://digitalcommons.unl.edu/archengdiss/29/

Assembled in 2014 by Amanda.Blair.Lind@gmail.com