Log in
The Spherical Sound Field
The below links show several Animations to the spherical base solutions (singular for outgoing, regular for incoming waves) up to n=3.
- Animated Spherical Harmonic Vibrations
Below, you will find the Spherical Harmonics animated as modes of vibration on a spherical surface. The index n counts the nodal circles on the sphere, and |m| describes how many of these nodal circles lie on the longitude (running over south+north pole of the sphere). In the real-valued case the shapes for negative ms are just 2*pi/(|m|+1)-rotated versions of the positive ones. In the complex-valued case, they are complex conjugates.
- Animated Radial Propagation Terms
In the link below, the radial propagation terms, that radiate the spherical harmonics either for incoming or outgoing waves. The corresponding functions are either
- spherical Bessel functions jn(kr) for incoming waves are standing waves, as their radial part is purely real-valued.
- spherical Hankel functions hn(kr) for outgoing travelling waves, with a singularity at r=0, and the fulfilling the Sommerfeld radiation condition p=-i*v at r=infinity.
- Animated Spherical Base Solutions
These links navigate you to the animated spherical base solutions. I chose r0=1 and k=2*pi. You will find the iso-surfaces of these Solutions for the positive and negative half-wave in the range r=1...4.
- Wave-Spectrum Truncation Effects
These links navigate you to the animated plane-wave and Green's function representation in the spherical base solutions, truncated at some order n<=N. All animations are for rotationally symmetric settings in the x-z plane.
Franz Zotter, 2006. updated 2008.