Waves
Class 11 · Waves

Phase Difference

φ = (2π/λ) Δx — visualize phase vs path.

Key Notes

01

Phase difference Δφ: how much one oscillation leads or lags another (in radians or degrees).

02

Two waves in PHASE (Δφ = 0, 2π, 4π…): crests align, displacements add (constructive).

03

Two waves OUT OF PHASE by π (180°): crest of one aligns with trough of other, cancel.

04

Phase difference from path difference: Δφ = (2π/λ)·Δx.

05

Constructive interference: Δφ = 2nπ (path difference = nλ).

06

Destructive: Δφ = (2n+1)π (path difference = (n+½)λ).

07

On phasor diagram: two oscillations are vectors with angle Δφ between them.

08

Phase difference can be due to: PATH difference, initial PHASE offset, REFRACTION through different medium, REFLECTION at boundary (which can add π).

Formulas

Path-to-phase

Most common cause of phase difference: spatial separation.

Time-to-phase

Phase changes by ω·Δt over time Δt.

Constructive interference

Path difference = nλ.

Destructive interference

Path difference = (n+½)λ.

Important Points

In phase (Δφ = 0): waves add ⇒ constructive ⇒ 2A.

Antiphase (Δφ = π): waves cancel ⇒ destructive ⇒ 0.

Phase difference is BETWEEN two waves — not absolute.

Path difference Δx and phase difference Δφ are linked by Δφ = 2π·Δx/λ.

Reflection at a denser medium adds π to phase. Important in thin-film interference.

Maxwell's electromagnetic theory: E and B are exactly IN PHASE in free space.

Phase Difference notes from sciphylab (also known as SciPhy, SciPhy Lab, SciPhy Labs, Physics Lab). Class 11 physics revision for JEE Mains, JEE Advanced, NEET UG, AP Physics 1/2/C, SAT, and CUET-UG.