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 plane-wave and point-source sound fields truncated at different orders n.
The table shows several animations of an N-truncated 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 wave-length
A very interesting fact when designing appropriate playback for a big sweet-spot.
| 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.