Explore constructive and destructive interference from two wave sources. Adjust frequency, phase, and source separation to reveal interference patterns, nodal lines, and standing waves.
When two waves overlap, their amplitudes add: y_total = A·sin(kr₁ − ωt) + A·sin(kr₂ − ωt + φ). Constructive interference occurs when |r₁−r₂| = nλ (path difference is integer wavelengths). Destructive interference when |r₁−r₂| = (n+½)λ. The 2D ripple tank shows brighter regions where waves reinforce and darker regions where they cancel.
For two point sources, intensity I ∝ cos²(πd·sinθ/λ) at angle θ from the centre. Young's double-slit experiment (1801) demonstrated the wave nature of light using exactly this geometry. The fringe spacing Δy = λL/d (L=screen distance, d=slit separation). Same physics governs radio antennas, sonar arrays, and optical interferometers.
When two identical waves travel in opposite directions, they form a standing wave: y = 2A·cos(kx)·sin(ωt). Nodes (always zero amplitude) are fixed in space at kx = (n+½)π. Anti-nodes have maximum amplitude. Musical instruments, microwave cavities, and laser resonators all use standing waves. In this sim, set phase = π to see the standing wave pattern.