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In case of symmetry around a point we can consider a sphere on whose surface points the waves are equidistant. But how to determine the wavefront around a linear source or a cylinder or triangle or of these or of an complex figure. Should I get the symmetry around every every point and integrate that? How to do it? And is there any alternative process to find it? Please help!

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For an alternate process: According to Huygens Principle the wavefront at time $t$ would be the envelope (or tangent surface) of all the Huygens wavelets originating from each point on the surface of the 'complex figure'. The radius of the wavelets would be $ct$.

For an approximate graphical solution, you can draw a figure and work out the results for the 'wavefront' by drawing circles of radius ct centered at closely spaced points on the 'complex figure' and then draw their tangent surface.

Note that the complete 'wavefield' is more involved. The 'wavefront' is the furthest extent of the wave, which is governed by causality. The 'wavefield' includes what follows after the 'wavefront'.

Google Huygens Principle to get images and further explanation. The images illustrate use of Huygens Principle.

Re. your "Should I get the symmetry around every every point and integrate that? How to do it?": To solve for the wavefield of a geometrically complex source using math would involve numerically solving Kirchoff's or Poisson's formula--you can Google that too.

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