The Physics
Opus in profectus

Diffraction & Interference (Sound)

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Nodal lines are hyperbolas. Think about it, the definition of a hyperbola is the locus of all points whose distance to two fixed points have a constant difference. At distances much greater than the wavelength, the nodal lines appear as straight radial lines.

Path length difference

constructive destructive
nλ = Δℓ (n + ½)λ = Δℓ

General equation

constructive destructive
nλ = d sin θ (n + ½)λ = d sin θ

Small angle approximation

constructive destructive
nλ  ≈  x
d L
(n + ½)λ  ≈  x
d L


n = 0, 1, 2, 3,…

is the order

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