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Waves and Optics

Propagation of Sound and Light Waves

This page explains concepts at college level in the field of wave propagation. The sound and light waves have been clubbed together to highlight lot of similarity in concepts dealing with wave phenomena such as reflection, transmission, interferences and diffraction.

Analogy and similarity between light and sound waves

Phenomena Sound Waves Light Waves
Equation of wave y = A sinω(t - x/v) E = E0 sinω(t - x/v)
Speed of wave v = [γ*RT]0.5 in air,
v = [B / ρ]0.5-liquid, v = [Y / ρ]0.5-solid
v = c / μ
Path difference
Multiple of wave-length
Physical distance between sources
Phase difference
Multiple of 2π [ = 1 cycle]
δ = Δx * 2π/λ δ = Δx * 2π/λ
Constructive Interference Maxima:
Δx = n * λ or δ = 2nπ
Bright fringes:
Δx = n * λ or δ = 2nπ
Destructive Interference Minima:
Δx = (2n+1) * λ/2 or δ = (2n + 1)π
Dark fringes:
Δx = (2n+1) * λ/2 or δ = (2n + 1)π

Diffraction and Interference

For example, refer to the interference of waves (including diffraction in case of light). The maxima and minima of sound waves are analogous to the bright and dark fringes and their location can be determined in similar ways.
Diffraction and interference of sound and light waves
The path difference is given by Δx = d * sinθ ≈ d * tanθ as sinθ ≈ = tanθ for small values of θ.

Note that distance between two consecutive maxima or consecutive minima of sound wave is analogous to the distance between centres of consecutive dark fringes or bright fringes. Note the symmetry of the geometry and wave transmission phenomena. For light wave, the symmetry plane can be also treated as a plane mirror described as follows:
Symmetry in diffraction of light waves

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