2. Wave Motion

The relationship between Path Difference and Phase Difference

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 DifferencePhase DifferenceTime Difference
λ × [Δϕ/2π]Δϕ[Δϕ/2π] × T
λ × [ΔT/T]2π × [ΔT/T]ΔT

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