Fields with limited order
The spherical basis solutions can be used to represent sound fields entirely only when the indices n and m are complete. In practice, it is convenient, sometimes numerically necessary to limit the index n to a finite order. The following animations show planewave and pointsource sound fields truncated at different orders n.
The table shows several animations of an Ntruncated representation of a plane wave and a Green's function. A rough rule of thumb:
We need an increase of the order by 6 for to increase the radius of accurate representation by one wavelength
A very interesting fact when designing appropriate playback for a big sweetspot.
plane wave  Green's function at z/lambda=2  
N=0  note that this column uses all two kinds of base solutions


N=1  
N=3  
N=6  
N=13 
Franz Zotter, 2008.