Spherical harmonics

You can consider the vibrating bubbles below, e.g., as the sound particle velocity at a certain fixed radius r in the sound field. The spherical harmonics have two indices. n determines how many nodal circles the spherical harmonic modes have, and |m| counts how many of them run through north and south pole. Therefore it is clear that the spherical harmonics can be seen as the spatial resolution. Another nice property: they are orthogonal; e.g. only the first one has a non-zero mean value.
real-valued spherical harmonics