three.js webgl - multiple elements with text

three.js - multiple elements with text - webgl

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

\frac{\partial^{2} u}{\partial r^{2}} - \frac{1}{c^{2}} \cdot \frac{\partial^{2} u}{\partial t^{2}} = 0

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

u (r, t) = \sin (k r \pm ω t)

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

\frac{\partial^{2} u}{\partial r^{2}} + \frac{1}{r} \cdot \frac{\partial u}{\partial r} - \frac{1}{c^{2}} \cdot \frac{\partial^{2} u}{\partial t^{2}} = 0

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

u (r, t) = \frac{\sin (k r \pm ω t)}{\sqrt{r}}

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

\frac{\partial^{2} u}{\partial r^{2}} + \frac{2}{r} \cdot \frac{\partial u}{\partial r} - \frac{1}{c^{2}} \cdot \frac{\partial^{2} u}{\partial t^{2}} = 0

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

u (r, t) = \frac{\sin (k r \pm ω t)}{r}

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.