Superposition
When two waves meet, their displacements add together at each point — this is the principle of superposition. The combined effect is called interference. To produce a steady, observable pattern the two sources must be coherent: same frequency and a constant phase difference.
Constructive and destructive interference
- Constructive interference: two waves arrive in phase (crest meets crest). Displacements add → a larger amplitude (a bright fringe / loud sound / big wave).
- Destructive interference: two waves arrive out of phase (crest meets trough). Displacements cancel → zero or small amplitude (a dark fringe / quiet region).
Key formula / Key formula
For two-source interference: λ = ax / D
where a = distance between the two sources (slit separation), x = distance between adjacent bright fringes, D = distance from the sources to the screen.
Rearranged: x = λD / a.
Worked example
Two coherent sources are 0.50 mm apart. On a screen 2.0 m away the bright fringes are 2.4 mm apart. Find the wavelength.
Convert units: a = 0.50 mm = 0.0005 m, x = 2.4 mm = 0.0024 m, D = 2.0 m.
λ = ax / D = (0.0005 × 0.0024) / 2.0 = 6.0 × 10⁻⁷ m = 600 nm.
Patterns and uses
In a ripple tank, two dippers produce a pattern of lines of constructive interference (large waves) separated by lines of destructive interference (still water). The same idea explains the bright and dark fringes in Young's double-slit experiment for light, showing that light behaves as a wave.
Remember
- Constructive: in phase, amplitudes add.
- Destructive: out of phase, amplitudes cancel.
- Use consistent SI units in λ = ax/D (convert mm to m).