Ripple Tank (Wave Interference)

Compare interference from two in-phase sources with diffraction through one or two openings. Choose an experiment and select Run. Longer wavelength generally spreads fringes; wider source or slit separation brings fringes closer. This is a finite scalar-wave teaching model, not a calibrated water-depth or optical-power calculation.

Geometry. Lengths are in grid cells. Even slit widths and separations preserve exact reflection symmetry about the centre of the 200-row grid. The two sources each occupy two adjacent cells; the other modes use a finite vertical source line. A slit width must be smaller than the separation, and the sum must not exceed 168 cells. Changing wavelength, geometry or source clears the old experiment. Playback speed and screen visibility preserve its field.

Model and boundaries. The solver uses centred differences for u_tt + 2σu_t = c²(u_xx + u_yy), with Δx = Δy = Δt = 1 and c² = 0.45. Thus Cx² + Cy² = 0.9 < 1, the two-dimensional CFL bound. The three-cell partition and outer edge impose u = 0: reflections reverse sign, unlike a rigid-wall Neumann condition. An external layer of h = max(32, ceil(2λ)) cells surrounds the visible tank. Its quadratic damping rises from zero at the visible edge to σ = 4.8/h at the outer boundary. This empirical absorber reduces returning waves; it is not a perfectly matched layer. The partition extends through the layer to prevent waves bypassing its ends. Residual reflections, finite source length and grid dispersion remain. No wave displacement is clipped or renormalized.

Time and measurement. One step advances exactly Δt = 1. The source has period T = λ/c and ramps up over two periods. It prescribes displacement at its cells; it is not a force or power input. The plane source extends outside the visible tank, ending 16 cells before the outer boundary. Reflection from the partition can produce transient resonances under continuous drive. Entered λ is the continuum wavelength; numerical dispersion changes its grid representation slightly. Screen sampling starts after the direct source-to-screen transit estimate plus four periods. It uses an explicitly divided moving mean of u², with a window rounded up to eight periods. This warm-up is a convention, not a guarantee of steady state. The screen covers all 200 visible rows at x = 292, within the undamped tank. It reports relative squared amplitude, not energy flux or watts. Clear average empties only the samples. The displacement palette stays fixed; the profile axis adjusts to its labelled numerical range.

Playback. The requested number of numerical steps per second is independent of display refresh rate. Under load playback slows; it does not enlarge the time step. Hidden tabs and hidden tool views suspend it. With reduced motion enabled, Run first prepares a paused field. With the source off, the initially still field remains still.

Reference. Langtangen and Linge, finite-difference wave dispersion and 2D stability; damping and reflecting boundaries.