Press the button: minimum phase speed, group speed and the number of interference minima are compared with closed-form values.

Ripples on shallow-tank-scale water are restored by both gravity and surface tension. The dispersion relation for deep water is w^2 = g k + (sigma / rho) k^3 with sigma = 72 mN/m and rho = 1 g/cm3 (CGS units here). For long waves gravity dominates and the phase speed c = sqrt(g/k + sigma k / rho) falls as k grows; for short waves surface tension dominates and c rises. The minimum is c_min = (4 sigma g / rho)^(1/4) = 23.1 cm/s at wavelength 2 pi sqrt(sigma / (rho g)) = 1.71 cm: no ripple on clean water travels slower. The group speed (energy speed) is c_g = (g + 3 sigma k^2 / rho) / (2 w).

Two dippers vibrating at the same frequency radiate circular waves whose height falls roughly like 1/sqrt(r) and is damped by viscosity (a decay length is used). Where the path difference r1 - r2 equals an odd number of half wavelengths the waves cancel: these are the hyperbolic nodal lines. Changing the frequency changes the wavelength (through the dispersion relation) and therefore the number of nodal lines; changing the second dipper's phase shifts them sideways.

Simplifications: linear waves on deep, clean water; point sources; an empirical decay length; the picture is time-stretched so the oscillation is visible. Same physics as the 3D page.