Explain interference, coherence and fringe conditions
Use coherent sources and superposition to interpret stable reinforcement and cancellation patterns.
AS Level; Cambridge International Physics 9702, 2025–2027 syllabus, Topic 8. These original models and calculations are study aids; full timed assessment, supervised practical competence and human subject-teacher review remain outstanding.
Before you begin
- Use wavelength, frequency, phase difference, trigonometry and consistent SI units.
Work on paper. Try each question before revealing help, and explain why your method works.
Quick readiness check
What is required of coherent sources?
What you will learn
- Define interference and coherence
- Describe two-source demonstrations with water, sound, light and microwaves
- State the conditions needed for stable two-source fringes
Interference is a pattern from superposition
Interference is the redistribution of resultant amplitude when waves superpose. At a position where path difference is an integer number of wavelengths, the waves arrive in phase and reinforce. A half-integer wavelength path difference gives antiphase arrival and cancellation for equal amplitudes.
Coherent sources have the same frequency and a constant phase difference. Coherence makes the maxima and minima remain at fixed positions; independent sources with changing phase generally do not give a stable fringe pattern.
Demonstrate stable two-source interference
Two point sources driven from the same water-wave vibrator can make an interference pattern visible in a ripple tank. Two loudspeakers driven by one signal can produce regions of louder and quieter sound; coherent light sources or coherent microwave sources can also demonstrate two-source interference.
For stable two-source fringes, the sources must be coherent and overlap at the observation region. For clear sustained contrast, the waves should have comparable amplitudes and the apparatus must not drift; use a screen or detector to compare maxima and minima across position.
Pause and explain
What path difference gives antiphase arrival?
Worked example
At a point, two coherent waves have path difference 2λ. State whether they arrive in phase or antiphase.
Show the worked solution
- A whole-number wavelength path difference is an integer-cycle phase shift.
- Here n = 2.
- An integer-cycle difference means the waves are in phase.
Answer They arrive in phase and reinforce.
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Test this topic →From guided practice to a new situation
Write your answer and reasoning first. Use a hint only if you are stuck. The model solution is for self-checking; your written work is not automatically marked.
Two coherent sources produce waves that travel path lengths differing by 3λ at a point. State the phase relationship and expected result for equal amplitudes.
Give me a hint
A whole number of wavelengths is a whole number of cycles.
Compare my reasoning
- Path difference = 3λ, an integer multiple of λ.
- The waves arrive in phase.
- For equal amplitudes they reinforce to a maximum.
In phase; constructive interference gives a maximum for equal amplitudes.
Look for these in your work
- Integer-cycle condition used
- Phase stated
- Amplitude condition included
A ripple tank has two point sources driven at the same frequency by one vibrator. Explain why this arrangement can produce stationary maxima and minima.
Give me a hint
Connect the shared driver to phase stability and then to superposition.
Compare my reasoning
- A common oscillator fixes the frequency and maintains a constant phase difference.
- The waves overlap in the tank and superpose.
- Different path differences produce stable reinforcement and cancellation positions.
The common source makes the waves coherent; their overlapping waves reinforce or cancel at fixed path differences, creating stable maxima and minima.
Look for these in your work
- Coherence explained
- Overlap identified
- Fixed pattern reasoned
A student uses two independent loudspeakers with frequencies that drift slightly and sees no stable quiet/loud map. Explain the limitation and propose a better source arrangement.
Give me a hint
Consider whether the relative phase remains constant over time.
Compare my reasoning
- A frequency difference makes relative phase change with time.
- Maxima and minima then shift, so the pattern is not stable.
- Drive both speakers from the same signal generator to make coherent sources.
The independent frequencies do not maintain a constant phase difference, so the interference pattern drifts. Use a common signal generator for both speakers.
Look for these in your work
- Phase drift identified
- Pattern instability linked
- Coherent replacement proposed
Common mistakes
- Calling any two sources coherent merely because their frequencies are similar
- Treating a fixed phase difference as a changing random difference
- Saying all destructive interference requires zero amplitude sources
What can you explain now?
What is required of coherent sources?
Compare with the explanation
They have the same frequency and constant phase difference
These conditions allow a stable phase relationship.
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Make it stick
Why does a stable interference map need coherence, rather than frequency similarity alone?
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