Section 1 of 5The Principle
Superposition explains how waves combine, from noise-cancelling headphones to the patterns made by light.
Statement
- When two or more waves meet at a point, the resultant displacement is the vector sum of the displacements of each wave there.
Instantaneous
- The addition applies at every instant, so the resultant changes as the waves continue to move.
Passing through
- After meeting, the waves continue as before, each unaffected by the encounter.
Signs
- Displacements in opposite directions have opposite signs, so they partly or fully cancel.
Section 2 of 5Everyday Examples
Everyday Examples
Reflection
- A wave reflected at a boundary overlaps the incoming wave, and the two combine along the same path.
Sound
- Loudspeakers can produce regions of loud and quiet sound where their waves reinforce or cancel.
Water
- Ripples from two sources cross and form a pattern of calm and disturbed regions.
Instruments
- The notes of organ pipes and strings come from waves that reflect and overlap along the instrument.
Section 3 of 5Experiments
1
In a resonance tube, sound waves reflect from the closed end and combine with the oncoming waves to give a stationary wave.
2
Two loudspeakers driven by one signal generator produce a pattern of loud and quiet positions when a microphone is moved in front.
3
Two microwave transmitters, or one transmitter with a double slit, give maxima and minima on a receiver moved along a line.
4
Light passing through two narrow slits (Young's double slit) or a diffraction grating produces bright and dark fringes.
5
Each experiment relies on the same principle: the displacements at each point add.
Section 4 of 5Worked Example
Question
- At one instant and at one point, two waves would separately produce displacements of +3.0 mm and −1.0 mm.
- What is the resultant displacement, and what is it if the second becomes +1.5 mm?
- Add the displacements+3.0 + (−1.0) = +2.0 mm.
- For the second case+3.0 + 1.5 = +4.5 mm.
Answer +2.0 mm in the first case and +4.5 mm in the second.
Section 5 of 5Exam Checklist & Tips
4.9.1 – Key Points for the Exam
- Superposition The resultant displacement is the sum of the displacements of the waves present at that point.
- Resultant The single displacement that results from combining several waves.
- Stationary wave A wave pattern formed by superposition of two waves travelling in opposite directions.
- Fringe A bright or dark band formed by interference of light.
Common Mistakes
- Adding amplitudes only, rather than displacements with their correct signs.
- Thinking waves permanently destroy each other when they cancel; they pass through unchanged.
- Believing superposition applies only to light.
- Forgetting the principle applies at every instant, not only at the peak.