Superposition, interference and path differenceEdexcel International A Level Physics: Revision notes
Section 1
Wavefronts, phase and coherence
A wavefront is a line or surface joining points on a wave that are in phase, for example all the crests of a ripple. Wavefronts spread out from a source and are perpendicular to the direction of travel.
Phase describes the position in the oscillation cycle. Two points are in phase when they are at the same stage of the cycle (phase difference 0, 2π, 4π...) and in antiphase when they are half a cycle apart (π, 3π...).
Two sources are coherent if they emit waves of the same frequency with a constant phase difference.
Coherent does not mean in phase. Coherent sources have a constant phase difference, which may be any value.
Section 2
Superposition and interference
Superposition: when two or more waves meet, the resultant displacement at a point is the sum of the displacements of the individual waves at that point.
Interference is the effect of superposition:
- Constructive interference: the waves arrive in phase, so the amplitude is a maximum.
- Destructive interference: the waves arrive in antiphase, so the amplitude is a minimum (zero if the amplitudes are equal).
A stable pattern of maxima and minima needs coherent sources, as then the positions of the maxima and minima do not move.
Section 3
Path difference
The path difference is the difference in the distances travelled by two waves from their sources to the same point.
For two sources that emit in phase:
- Path difference = nλ (n = 0, 1, 2...): waves arrive in phase, constructive interference.
- Path difference = (n + ½)λ: waves arrive in antiphase, destructive interference.
Worked example: a listener is 3.00 m from speaker X and 3.60 m from speaker Y, with λ = 0.40 m. The path difference is 0.60 m = 1.5λ, so the sound is a minimum.
Divide the path difference by the wavelength. A whole number means loud (maximum); a half-integer means quiet (minimum), for sources in phase.
Section 4
Phase difference and path difference
A path difference of one wavelength corresponds to a phase difference of one full cycle, 2π rad (360°). So:
phase difference φ = 2π × (path difference) / λ (in radians)
or φ = 360° × (path difference) / λ in degrees.
Worked example: two points on a wave of wavelength 0.90 m are 0.15 m apart along its direction of travel. φ = 2π × 0.15 / 0.90 = π/3 rad (60°).
Points half a wavelength apart have φ = π (antiphase); points one wavelength apart have φ = 2π (in phase).
Must Know
- Superposition: add the displacements
- Coherent: same frequency, constant phase difference
- Path difference nλ: constructive; (n + ½)λ: destructive (sources in phase)
- φ = 2π × path difference / λ
- Stable interference needs coherent sources
That's the notes covered.
Carry on to the next subtopic.
Exam questions on Superposition, interference and path difference
- Two small loudspeakers, X and Y, are connected to the same signal generator and emit sound of wavelength 0.40 m in phase. A listener stands at a point P that is 3.00 m from X and 3.60 m from Y.Explain, using ideas of path difference and phase, why the sound at P is not loud.2 marks
- A progressive wave has a wavelength of 0.90 m and a frequency of 120 Hz. Two points A and B lie along the direction of travel of the wave, 0.15 m apart.Calculate the minimum separation of two points on the wave that are exactly in antiphase.2 marks
- Two identical dippers, S₁ and S₂, vibrate in phase at 8.0 Hz in a ripple tank, each producing circular waves of wavelength 2.5 cm. A point Q on the water surface is 20.0 cm from S₁ and 25.0 cm from S₂.State what is meant by superposition, and explain why the dippers must be coherent to produce a stable interference pattern.3 marks
Written by the Exaim team, led by Shaun Daswani (Head of Upper Secondary, Improve ME Institute; MSc Financial Mathematics, Imperial College London; BSc, UCL) and Jason Daswani (operational lead, Improve ME Institute; LSE).