Phase difference (definition)
● VERBATIM — examined word-for-wordPhase difference is a measure of the fraction of a cycle by which one oscillation leads or lags another, expressed as an angle, where one complete cycle corresponds to 2π rad (360°).
Δφ = 2π × (fraction of a cycle) = 2π (Δt/T) = 2π (Δx/λ)What this actually means
Phase difference is an angle, so it needs rad or degrees. Writing a bare number loses the unit mark.
It works both between two separate waves at one point, and between two points on the same wave. The formula is the same: convert the offset into a fraction of a cycle, then multiply by 2π.
Phase differences are only defined modulo 2π. A phase difference of 3π is physically the same as π, so waves 3π apart are antiphase, not something new.
In phase means Δφ = 0, 2π, 4π …, and antiphase (out of phase) means Δφ = π, 3π, 5π …. Anything between is just a partial reinforcement.
When the question gives a time offset, use Δt/T. When it gives a distance along the same wave, use Δx/λ. When it gives a path difference from two sources, use path difference divided by λ.
Quoting a phase difference as a plain number or as a distance instead of an angle in rad or degrees.
Prove it — watch it be true
- In the two-sines mode, set Δφ to π/2 with the slider and read the shift between the two curves.
- Confirm that shift is a quarter of a wavelength on the position axis.
- Set Δφ to 3π and confirm the traces look identical to Δφ = π.