Practice question · Sort into groups
Two identical waves overlap. Sort each described situation by the kind of interference it produces.
Groups: Constructive · Destructive
- Trough meets trough
- Crest meets trough
- A noise-cancelling headphone adds an inverted copy of the incoming sound
- Two speakers in step reinforce the sound at a point
- Crest meets crest
Hints
- Overlapping waves simply add their displacements at each point.
- Two troughs together make a deeper trough, which is still reinforcement.
Show the answer
Constructive: Crest meets crest, Trough meets trough, Two speakers in step reinforce the sound at a point
Destructive: Crest meets trough, A noise-cancelling headphone adds an inverted copy of the incoming sound
Why
Like displacements reinforce and opposite ones cancel, so trough meeting trough is constructive even though the result points downward. Inverting a signal and adding it is destructive interference by design, the whole principle of active noise cancellation.
Practise Oscillations and Waves
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