three.js - multiple elements with text - webgl

Sound waves whose geometry is determined by a single dimension, plane waves, obey the wave equation

∂^{2}*u*
∂*r*^{2}
−
1^{}
*c*^{2}
∂^{2}*u*
∂*t*^{2}
= 0

where *c* designates the speed of sound in the medium. The monochromatic solution for plane waves will be taken to be

where ω is the frequency and *k*=ω/*c* is the wave number. The sign chosen in the argument determines the direction of movement of the waves.

Here is a plane wave moving on a three-dimensional lattice of atoms:

Here is a plane wave moving through a three-dimensional random distribution of molecules:

Sound waves whose geometry is determined by two dimensions, cylindrical waves, obey the wave equation

∂^{2}*u*
∂*r*^{2}
+
1
*r*
∂*u*
∂*r*
−
1^{}
*c*^{2}
∂^{2}*u*
∂*t*^{2}
= 0

The monochromatic solution for cylindrical sound waves will be taken to be

Here is a cylindrical wave moving on a three-dimensional lattice of atoms:

Here is a cylindrical wave moving through a three-dimensional random distribution of molecules:

Sound waves whose geometry is determined by three dimensions, spherical waves, obey the wave equation

∂^{2}*u*
∂*r*^{2}
+
2
*r*
∂*u*
∂*r*
−
1^{}
*c*^{2}
∂^{2}*u*
∂*t*^{2}
= 0

The monochromatic solution for spherical sound waves will be taken to be

Here is a spherical wave moving on a three-dimensional lattice of atoms:

Here is a spherical wave moving through a three-dimensional random distribution of molecules:

The mathematical description of sound waves can be carried to higher dimensions, but one needs to wait for Four.js and its higher-dimensional successors to attempt visualizations.