4.9.4Electrons, Waves and Photons
Two-Source Interference — OCR A Level Physics A H556 Revision Notes & Topical Questions
5 min read 5 parts Lesson 57 of 62 Unit quiz
Section 1 of 5Conditions and Meaning
A steady, stable pattern of loud and quiet regions only appears when the two sources are coherent.
Coherent sources
- Two sources are coherent when they keep a constant phase difference,
- which in practice means they share the same frequency and are driven from one oscillator.
Overlap
- Where waves from both sources arrive at one point, the principle of superposition says the resultant displacement is the sum of the individual displacements.
Constructive
- Waves arriving in phase add to give a maximum, such as loud sound or a strong microwave signal.
Destructive
- Waves arriving in antiphase cancel to give a minimum, which is a quiet point or a near-zero detector reading.
Section 2 of 5Path Difference Rule
Path Difference Rule
Path difference
- This is the difference between the distances from the two sources to the point being considered, measured in metres.
Maximum condition
- For two sources vibrating in phase, a maximum occurs where the path difference is a whole number of wavelengths: nλ.
Minimum condition
- For in-phase sources, a minimum occurs where the path difference is an odd number of half wavelengths: (n + ½)λ.
Central maximum
- Points equidistant from both sources have zero path difference, so the waves always arrive in phase and the centre is a maximum.
| Path difference | Phase relationship | Result |
|---|---|---|
| 0, λ, 2λ … | In phase | Constructive: maximum |
| ½λ, 1½λ, 2½λ … | Antiphase | Destructive: minimum |
Section 3 of 5Demonstrations
1
Connect two loudspeakers to one signal generator and walk along a line parallel to them, hearing loud and quiet positions alternate.
2
Place a microwave transmitter behind two slits in a metal sheet and move a detector along a line in front of the slits.
3
The detector reading rises to a maximum where the waves reinforce and falls close to zero where they cancel out.
4
Noise-cancelling headphones apply the same idea by producing sound that arrives in antiphase with unwanted noise.
5
In an answer always describe the effect in terms of the signal or loudness actually being measured, not just "interference".
Section 4 of 5Worked Example
Question
- Two loudspeakers S₁ and S₂ emit in-phase sound of frequency 1000 Hz.
- The speed of sound is 340 m/s.
- A point P is 4.00 m from S₁ and 4.51 m from S₂.
- State whether P is a loud or quiet position.
- Wavelength λ = v ÷ f = 340 ÷ 1000 = 0.34 m.
- Path difference = 4.51 − 4.00 = 0.51 m.
- Number of wavelengths = 0.51 ÷ 0.34 = 1.5, an odd number of half wavelengths.
Answer The waves arrive in antiphase, so P is a quiet position (destructive interference).
Section 5 of 5Exam Checklist & Tips
4.9.4 – Key Points for the Exam
- Coherent Describes sources with a constant phase difference, so the interference pattern does not change with time.
- Path difference The difference in the distances travelled by two waves to reach the same point.
- Constructive interference Superposition of waves in phase, giving a resultant of larger amplitude.
- Destructive interference Superposition of waves in antiphase, giving a resultant of smaller or zero amplitude.
Common Mistakes
- Saying the waves "destroy" each other; the energy is redistributed to the maxima, not lost.
- Using nλ for a minimum; minima need an odd number of half wavelengths.
- Forgetting that two separate light bulbs are not coherent, so no stable pattern is seen.
- Writing "louder" or "quieter" for light or microwaves instead of brighter, darker or stronger signal.
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