2D Wave Table

The ripple tank

The ripple tank is one of physics’ most powerful teaching instruments, a shallow tray of water in which wave behaviour can be made directly visible. When a point source vibrates at the surface, circular wavefronts propagate outward; when two sources operate side by side, their waves superpose — constructive interference builds peaks where crests meet crests, and destructive interference creates quiet nodal lines where a crest meets a trough. These interference patterns, easily observed in water, are identical in structure to those produced by light, sound, radio waves, and even quantum probability amplitudes. The mathematical description is the same two-dimensional wave equation in every case: ∂²u/∂t² = c²∇²u, differing only in what u represents (water height, air pressure, electric field strength, or wave-function amplitude) and the value of the propagation speed c.

Young’s double slit and the nature of light

In 1801, Thomas Young performed what Richard Feynman later called “the experiment that contains the only mystery of quantum mechanics.” By passing sunlight through two narrow, closely-spaced slits, Young observed alternating bright and dark fringes on a screen — an interference pattern impossible to explain if light consisted of particles (as Newton had proposed), but a natural consequence of wave superposition. The same pattern appears in this simulation when you place a barrier with two slits in front of a plane wave source. The angular positions of the bright fringes satisfy d sin θ = mλ, where d is the slit separation, λ the wavelength, and m an integer. What makes the result truly profound is that it holds even when individual photons or electrons pass through the slits one at a time — each particle somehow “interferes with itself,” building up the wave pattern over many detections. The ripple tank makes this wave behaviour viscerally intuitive: you can watch the nodal lines form in real time and see how changing frequency or slit width reshapes the pattern.

Huygens’ principle and diffraction

Christiaan Huygens proposed in 1678 that every point on a wavefront acts as a source of secondary spherical wavelets, and the new wavefront is the envelope of all these wavelets. This elegant geometric principle explains both reflection and refraction, and critically, it explains diffraction — the bending of waves around obstacles and through apertures. Diffraction effects become prominent when the aperture width is comparable to the wavelength: a slit much wider than λ casts a sharp shadow, but a slit on the order of λ produces wide spreading. In this simulation, you can verify this directly by drawing barriers with slits of varying width and observing how the diffraction pattern changes. The same physics explains why AM radio waves (wavelength ~300 m) bend around buildings while visible light (wavelength ~500 nm) does not, why harbour entrances diffract ocean swells, and why electron microscopes achieve resolution far beyond optical microscopes — by using “waves” with wavelengths thousands of times shorter than light.