Interactive 2D multi-source wave interference visualization: drag sources to observe constructive and destructive patterns
When multiple waves overlap in space, the displacement at any point equals the algebraic sum of individual waves: y_total = Σy_i. This is the superposition principle, the theoretical basis of interference.
When path difference Δr = nλ (n integer), waves add in phase for maximum amplitude — constructive interference. When Δr = (n+½)λ, waves cancel — destructive interference. In 2D patterns these appear as alternating bright/dark fringes or rings.
In the double-slit experiment, the path difference to a screen point is Δr ≈ d·sinθ. Bright fringes at Δr = nλ, dark at Δr = (n+½)λ. Fringe spacing Δy ≈ λL/d, proportional to wavelength and inversely to slit separation.
Thomas Young first confirmed the wave nature of light using double slits. Monochromatic light passing through two narrow slits produces alternating bright and dark interference fringes on a screen, enabling precise wavelength measurement.
Interference from an air film between a plano-convex lens and a flat glass plate produces concentric ring patterns. Ring radius r_n ∝ √n allows precise measurement of curvature radius or wavelength.
Colorful fringes on soap bubbles and oil films arise from interference between light reflected from the top and bottom surfaces. Optical path difference 2nd·cosθ varies with thickness and angle, producing different colors at different positions.
The Michelson interferometer measures nanometer-scale displacements, used in gravitational wave detection (LIGO), surface profilometry, and optical component testing.
Phased array radar uses interference from multiple antenna elements. By adjusting phases, the beam steers electronically without mechanical rotation. 5G Massive MIMO uses the same principle.
Active noise cancellation headphones emit anti-phase sound waves to destructively interfere with ambient noise. Concert hall design must control reflected sound interference for optimal acoustics.