Theme C — Wave Behaviour
C.3.6 Interference of Waves — IB Physics HL Revision Notes & Topical Questions
5 min read 11 parts Lesson 22 of 37 1 quiz
Curriculum Equation Key Wave Speed & Doppler Effect FormulasFast Exam Solution
v = f × λ | f_obs = f × (v ± v_o) / (v ∓ v_s) | T = 1 / f
Lesson summary
C.3.6 Interference of Waves — IB PHYSICS SL notes: Use path difference and phase difference to predict constructive and destructive interference from two coherent sources.Interference — the effect of superposition of waves from coherent sources, giving a stable pattern of reinfor…
- Ways to make it
- Intermediate points
- Constructive interference
- Difference from phase difference
- Phase difference link
- Constructive (maximum)
Part 1 of 9Double-source interference
Interference
- Interference the effect of superposition of waves from coherent sources, giving a stable pattern of reinforcement and cancellation
Ways to make it
- Ways to make it two coherent wave sources, or a single source passing through a double slit
Examples
- Examples a laser beam giving bright and dark fringes, two loudspeakers emitting coherent sound and microwaves diffracted through two slits
Coherence
- Coherence the waves must have the same frequency and a constant phase difference
- A sudden change of phase gives an inconsistent phase difference, so the pattern is lost.
Intermediate points
- Intermediate points where waves are neither in phase nor in antiphase the amplitude lies between the two extremes
Part 2 of 9In phase and in antiphase
1Constructive interference
- Constructive interference waves in phase meet peak-to-peak or trough-to-trough and add
- The resultant has double the amplitude for equal waves.
2Destructive interference
- Destructive interference waves in antiphase meet peak-to-trough and cancel
- The resultant has zero amplitude for equal waves.
Part 3 of 9Path difference
1Path difference
- Path difference the difference in the distances travelled by two waves from their sources to the point where they meet
- It is |S1P − S2P| in metres or in wavelengths.
2Difference from phase difference
- Difference from phase difference phase difference compares the phases of waves at a point,
- while path difference compares the distances they have travelled
3Phase difference link
- Phase difference link phase difference = 2π × /λ
- (path difference)
Part 4 of 9Conditions for interference
1Constructive (maximum)
- Constructive (maximum) path difference = nλ, where n = 0, 1, 2, 3 …
- The phase difference is 2πn.
2Destructive (minimum)
- Destructive (minimum) path difference = (n + ½)λ, so λ/2, 3λ/2, 5λ/2 …
- The phase difference is (2n + 1)π.
3Sources in antiphase
- Sources in antiphase the conditions swap
4Data booklet
- Data booklet these conditions are given, so you must apply them rather than memorise them
5Quick check
- Quick check find the path difference in wavelengths first
- A whole number gives a maximum.
- A half-odd number gives a minimum.
- Anything else gives an intermediate intensity.
Part 5 of 9Finding the type of interference on a diagram
1
Count the wavelengths from each source to the point, using crests on a wavefront diagram.
2
Subtract the two distances to get the path difference.
3
Compare it with nλ and (n + ½)λ and state n.
4
Decide whether the point is constructive or destructive.
- Wavefront diagrams
- constructive interference lies along lines where peak meets peak or trough meets trough
- Destructive interference lies where a peak meets a trough.
Part 6 of 9Patterns for water, sound and microwaves
Ripple tank
- Ripple tank two dippers driven together give lines of maximum disturbance and lines of near-calm water radiating from between the sources
Central line
- Central line the line equidistant from both sources is a maximum because the path difference is zero
Number of lines
- Number of lines maxima and minima alternate, with more lines when the source separation is larger compared with the wavelength
Loudspeakers
- Loudspeakers two speakers on one signal generator give alternating loud and quiet regions along a parallel line
- The effect is clearer in a room with few reflections and with a single-frequency sound.
Microwaves
- Microwaves a transmitter feeding two slits in a metal sheet gives a pattern that a probe receiver scans
Part 7 of 9Amplitude, intensity and energy
At a maximum
- At a maximum equal sources give double amplitude and four times the single-source intensity
At a minimum
- At a minimum equal amplitudes cancel completely, but unequal amplitudes leave a small residual
Energy
- Energy the pattern redistributes energy from the minima to the maxima without creating or destroying it
- On average the energy is just double that of one source.
Stability
- Stability if a source moves or its phase drifts, the lines sweep across and the pattern blurs
Part 8 of 9Measuring wavelength and applications
Measuring wavelength and applications
Measurement
- Measurement use a moving microphone or probe and the same spacing relation as for light
- Reading across many maxima and dividing by their number improves accuracy.
- Keep the two sources at the same amplitude to get clear minima.
Noise-cancelling headphones
- Noise-cancelling headphones they generate a wave in antiphase to ambient sound, giving destructive interference at the ear
Anti-reflective coatings
- Anti-reflective coatings light reflected from the two surfaces of a thin film is arranged to interfere destructively
Part 9 of 9More from the specification
1Snell's Law of Refraction
- When a wave travels across a boundary from one optical medium into another, its propagation speed changes;
- Snell's law relates the angle of incidence i and angle of refraction r by the refractive index: n₁ sin(i) = n₂ sin(r).
2Refractive Index and Wave Speed
- The absolute refractive index n of a transparent material is the ratio of wave speed in a vacuum c to its speed v in that medium (n = c / v).What the symbols mean: n = refractive index (no unit) · c = speed of light in a vacuum (3.00 × 108 m s−1) · v = speed of light in the material (m s−1)
3Total Internal Reflection and Critical Angle
- When light travels from an optically denser medium toward a less dense boundary, total internal reflection occurs if the angle of incidence exceeds the critical angle c,
- where sin(c) = n₂ / n₁.
4Refraction
- Change in direction of light when it changes speed between media.
5Boundary
- Surface between two media at which waves are partially reflected
6Medium
- Material through which light travels.
7Normal
- Line at 90° to a surface.
8Transmission
- Sending electricity along power cables from the power station to consumers.
9Refractive index
- Ratio of the speed of light in a vacuum to its speed in a material
10Critical angle
- Incline angle at which sliding just begins.
11Optically dense
- Having a high refractive index
12n1 sin θ1
n1 sin θ1 n2 sin θ2
What the symbols mean: n = refractive index (no unit) · i or θ1 = angle of incidence · r or θ2 = angle of refraction (both measured from the normal)
Key terms
| Term | Meaning |
|---|---|
| Interference | Superposition of coherent waves giving a stable pattern. |
| Path difference | Difference in the distances travelled by two waves to a point. |
| Constructive interference | Path difference of nλ. |
| Destructive interference | Path difference of (n + ½)λ. |
| Coherence | Same frequency and a constant phase difference. |
| Phase difference | Phase by which one wave leads the other. |
Avoid these mistakes
1
Using nλ for minima or (n + ½)λ for maxima.
2
Forgetting the central maximum at zero path difference.
3
Claiming energy is destroyed at minima — it goes to the maxima.
4
Using phase difference in degrees and radians interchangeably without converting.
5
Expecting a stable pattern from two ordinary light bulbs.
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