Superposition and diffraction · Year 12
When waves meet they superpose: crests on crests make bigger waves (constructive interference), crests on troughs cancel (destructive). Waves also spread out through gaps and around edges (diffraction), most when the gap is about one wavelength wide. These effects make the colours in soap bubbles, let us measure the wavelength of light, and create the notes on a guitar string.
Key facts
- Constructive: path difference = whole number of wavelengths. Destructive: an odd number of half-wavelengths.
- Diffraction is greatest when the gap is about the same size as the wavelength.
- Diffraction grating: d sin θ = nλ, with d = 1 ÷ (lines per metre). Highest order: n ≤ d ÷ λ.
- Double slit: fringe spacing w = λD ÷ s.
- Single slit minima: sin θ = mλ ÷ a.
- Stationary waves: nodes are half a wavelength apart; a string fixed at both ends with n loops has λ = 2L ÷ n.