02 · When two waves meet
Can two nonzero waves add to zero?
Predict the sum of equal waves with phase difference π.
- Select the interference experiment.
- Change relative phase from 0 to π ≈ 3.14 rad (180°).
- Compare both component waves and their sum.
Measurement
At a point inspect y₁, y₂ and y₁+y₂; measure resultant amplitude.
Linear displacements add. Equal contributions reinforce in phase and cancel in antiphase. Cancellation at a point does not destroy energy; spatial interference redistributes it. This principle connects to noise cancellation and antenna arrays. A phase-offset trace is a local slice, not a complete spatial radiation model.
A is each amplitude in m; Δφ in rad; path difference Δr and wavelength λ in m.
Worked example 1
For A=0.2 m and Δφ=0, resultant amplitude is 0.4 m.
Worked example 2
At Δφ=π equal contributions cancel. At Δφ=π/2 the resultant is 0.283 m.
Why do 0.2 m and 0.1 m antiphase waves not cancel completely?
Assumptions
Analytic linear educational model, not a numerical fluid solver. No damping, dispersion or nonlinear coupling.