Consider a progressive wave motion advancing in the positive direction of the x-axis
Path Difference vs Phase Difference
Let A and B be two points in the medium through which the wave passes.
The path difference between A and B is, x = x2 – x1
By the time the wave reaches B from A the phase of vibration of A has changed. The difference between the states of vibration of A and B is called phase difference (ΔO).
From this wave motion, if we consider any two consecutive crests c1 and c2, the path difference between them is λ, the time difference is T and the phase difference is 2π.
A path difference of (λ) corresponds to a phase difference of 2π, thus, a path difference (x) corresponds to the phase difference 2πr/λ.
Δϕ = (2πx)/λ = 2π/λ (path difference)
Where k = 2π/λ is called wave number or propagation constant of the wave motion.
A path difference (λ) corresponds to a time difference (T), therefore, a path difference (x) corresponds to a time difference of (x/λ)T.
The relations connecting the path difference, phase difference and time difference are given in the below table.
|Path Difference||Phase Difference||Time Difference|
|λ × [Δϕ/2π]||Δϕ||[Δϕ/2π] × T|
|λ × [ΔT/T]||2π × [ΔT/T]||ΔT|