Question

destructive interferance occurs when a trough meets up with another trough at a given location along the meduim

Answer 1

That statement is backwards.

- Constructive interference occurs when two waves are in phase at a point — e.g. a crest meets a crest or a trough meets a trough. Their displacements add, giving a larger amplitude (for identical amplitudes, they double).
- Destructive interference occurs when two waves are out of phase by π (180°) at a point — e.g. a crest meets a trough. Their displacements cancel (for equal amplitudes they cancel completely).

In equations: if y1 = A sin(kx − ωt) and y2 = A sin(kx − ωt + φ),
- total y = y1 + y2 = 2A cos(φ/2) sin(kx − ωt + φ/2).
- If φ = 0 (or 2πn), cos(φ/2) = ±1 → constructive.
- If φ = π (or (2n+1)π), cos(φ/2) = 0 → complete destructive.

For path difference Δ between two sources, destructive interference occurs when Δ = (n + 1/2)λ; constructive when Δ = nλ.

Also note: if amplitudes differ, interference is only partial (not complete cancellation). Examples: noise-cancelling headphones create destructive interference by producing sound waves phase-shifted by π relative to ambient noise.