In simple terms
A friendly intro before the formal notes — no formulas yet.
Interference
Cambridge 9702 Paper 2 — Interference (8.3). Senpai Corner diagram-backed pilot with premium structure and live visuals.
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8.3 Interference.
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Interference occurs when waves overlap and their resultant displacement is the sum of the displacement of each wave .
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Waves are coherent if they have the same frequency and constant phase difference .
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Two-source interference can be demonstrated in water using ripple tanks .
What this topic covers
The official Cambridge syllabus points this lesson works through.
- 8.3.1
Understand the terms interference and coherence
- 8.3.2
Show an understanding of experiments that demonstrate two-source interference using water waves in a ripple tank, sound, light and microwaves
- 8.3.3
Understand the conditions required if two-source interference fringes are to be observed
- 8.3.4
Recall and use for double-slit interference using light
Explore the concept
Use the live diagram, PhET or GeoGebra sim, and synced steps — play it, drag controls, or tap a step.
Step-synced diagram — highlights what to look for in the simulation above.
Two coherent sources emit waves in phase.
Two coherent sources emit waves in phase.
21 more simulations for this topic — run them in the Simulations section below
Simulations
Every simulation here runs the real model — try the steps on a card, then check what you see against the notes.
21 simulations · 5 to start with
Start herein this order — each one shows a different piece of the topic
- The Physics ClassroomStart here · 19702 8.3 · 9702 8.1 · IB C.3
Wave Addition
Two waves travel through the same medium; see the interference and the resultant at each point
Why this one: Resultant displacement is the sum of the two displacements at each point; shift one by λ/2 and they cancel.
Try this
- Add two waves of equal amplitude in phase.
- Shift one by half a wavelength.
- Change one amplitude and compare the resultant.
Look for The resultant displacement is the sum of the two displacements at each point.
Physics Interactives by The Physics Classroom · Licensed to MarkScheme (site terms otherwise permit linking only)
- The Physics ClassroomStart here · 29702 8.3 · IB C.3
Ripple Tank Simulator
Two point sources vibrate in a ripple tank; view the pattern and find the nodal and antinodal lines
Why this one: Trace a nodal line: path difference there is an odd number of half wavelengths.
Try this
- Start the sources and find a nodal line.
- Find an antinodal line.
- Count the nodal lines.
Look for Nodal lines lie where the path difference is an odd number of half wavelengths.
Physics Interactives by The Physics Classroom · Licensed to MarkScheme (site terms otherwise permit linking only)
- The Physics ClassroomStart here · 39702 8.3 · IB C.3
Young's Experiment
Make a few simple measurements on a two-slit pattern and calculate the wavelength of light
Why this one: Measure fringe spacing, slit separation and screen distance, then calculate λ as in the exam.
Try this
- Measure the fringe spacing on the pattern.
- Record the slit separation and the distance to the screen.
- Calculate the wavelength.
Look for Fringe spacing equals λD divided by the slit separation.
Physics Interactives by The Physics Classroom · Licensed to MarkScheme (site terms otherwise permit linking only)
- 3JCN PhysicsStart here · 49702 8.3 · IB C.3 · IB E.2
Young's Double-Slit Experiment
Change slit separation and wavelength; see the double-slit fringe pattern
Why this one: Double the slit separation and the fringe spacing halves; double λ and it doubles.
Try this
- Set a slit separation and wavelength and look at the fringe spacing.
- Double the slit separation and compare.
- Double the wavelength and compare.
Look for Fringe spacing equals λD / a, so it halves when the slit separation doubles and doubles with wavelength.
3JCN Physics Simulation by Thomas Nguyen · CC BY 4.0
- 3JCN PhysicsStart here · 59702 8.3 · 9702 7.1 · 9702 7.2
Wave Interference
Overlay two travelling waves with adjustable frequency and phase
Why this one: In phase the amplitudes add, in antiphase they cancel: coherence means a fixed phase difference.
Try this
- Overlay two waves with equal frequency and zero phase difference.
- Set a phase difference of 180° and compare the sum.
- Give the two waves slightly different frequencies and watch the sum.
Look for In phase the amplitudes add; in antiphase they cancel.
3JCN Physics Simulation by Thomas Nguyen · CC BY 4.0
More simulations16 more on this topic — core ones first
- oPhysicsCore9702 8.1 · 9702 8.3 · IB C.4
Superposition of Transverse Waves
Two transverse waves travelling in opposite directions; adjust speed/wavelength and see the resulting standing wave
Try this
- Run two waves of equal wavelength towards each other.
- Change the wavelength and count the nodes.
- Change the speed and watch the nodes.
Look for Nodes stay fixed half a wavelength apart whatever the speed; a shorter wavelength gives more nodes.
Simulation by Tom Walsh, oPhysics.com — made with GeoGebra · Licensed to MarkScheme (site: free for non-profit educational use; applets made with GeoGebra)
- oPhysicsCore9702 8.1 · 9702 8.3 · IB C.4
Interference & Standing Waves
Tutorial with applet: oppositely travelling waves of equal wavelength form a standing wave
Try this
- Run the two waves and watch the sum.
- Pause and locate the nodes.
- Measure the node spacing against the wavelength.
Look for Nodes are half a wavelength apart and never move.
Simulation by Tom Walsh, oPhysics.com — made with GeoGebra · Licensed to MarkScheme (site: free for non-profit educational use; applets made with GeoGebra)
- oPhysicsCore9702 8.3 · 9702 7.1 · IB C.3
Wave Pulse Interference and Superposition
Two wave pulses pass through each other; adjust heights/widths and watch the superposed sum
Try this
- Set both pulse heights positive and watch them cross.
- Make one height negative and cross again.
- Widen one pulse and compare the sum.
Look for The displacement at each point is the sum of the two pulses, and each pulse emerges unchanged after they cross.
Simulation by Tom Walsh, oPhysics.com — made with GeoGebra · Licensed to MarkScheme (site: free for non-profit educational use; applets made with GeoGebra)
- oPhysicsCore9702 8.3 · IB C.3
Wave Pulse Interference and Superposition 2
Two pulses on one string in opposite directions; the bottom string shows their point-by-point sum
Try this
- Run the pulses towards each other and watch the bottom string.
- Pause when the pulses overlap fully.
- Run again and compare the bottom string before and after.
Look for The bottom string is the point-by-point sum, so equal pulses of opposite sign cancel momentarily at full overlap.
Simulation by Tom Walsh, oPhysics.com — made with GeoGebra · Licensed to MarkScheme (site: free for non-profit educational use; applets made with GeoGebra)
- oPhysicsCore9702 8.3 · IB C.3
Wave Pulse Superposition Practice
Draw or pick two pulse shapes, predict the superposition and then check it
Try this
- Pick two pulse shapes and sketch their sum, then check it.
- Draw your own pulses with opposite signs and check.
- Try two pulses of different widths.
Look for The superposition at each point is the algebraic sum of the two pulse displacements.
Simulation by Tom Walsh, oPhysics.com — made with GeoGebra · Licensed to MarkScheme (site: free for non-profit educational use; applets made with GeoGebra)
- oPhysicsCore9702 8.3 · IB C.3
Wave Interference in 3D
Two-source surface-wave interference in 3D; adjust frequency, source separation and amplitude
Try this
- Increase the source separation and count the lines of calm water.
- Raise the frequency with the separation fixed.
- Change the amplitude.
Look for More nodal lines appear as separation grows or wavelength shrinks; amplitude changes the height but not the pattern.
Simulation by Tom Walsh, oPhysics.com — made with GeoGebra · Licensed to MarkScheme (site: free for non-profit educational use; applets made with GeoGebra)
Key formulas
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Full topic notes
Formal explanation with the rigour you need for the exam.
The Principle of Superposition
When two or more waves cross paths, their effects combine. At any point where they overlap, the resultant displacement is simply the vector sum of the individual displacements of each wave at that exact moment. This fundamental concept, the Principle of Superposition, dictates how waves interact and form interference patterns. For example, if a crest of amplitude +A meets another crest of amplitude +A, the resultant amplitude is +2A. If a crest of +A meets a trough of -A, the resultant amplitude is 0.
Coherence: The Key to Stable Interference
For us to observe a stable, unchanging interference pattern, the interacting waves must be coherent. This means they need to have the exact same frequency and wavelength, and crucially, maintain a constant phase relationship over time. If the phase difference changes randomly, the positions of constructive and destructive interference will also shift randomly, and no stable pattern will be seen. In practice, coherent sources are usually created by splitting a single wave into two or more parts, for example, by passing light from a single lamp or laser through two narrow slits.
8.3 Interference.
Interference occurs when waves overlap and their resultant displacement is the sum of the displacement of each wave .
Waves are coherent if they have the same frequency and constant phase difference .
Two-source interference can be demonstrated in water using ripple tanks .
Laser through two slits can also form interference patterns.
For two-source interference fringes to be observed, the sources of wave must be coherent and monochromatic (single wavelength).
Constructive and Destructive Interference
Interference can lead to two main outcomes. Constructive interference happens when waves meet perfectly in phase (crest to crest or trough to trough), resulting in a larger combined amplitude. Conversely, destructive interference occurs when waves meet exactly out of phase (antiphase), like a crest meeting a trough, leading to a minimum or even zero resultant amplitude.
Constructive: Waves meet in phase (peak-peak or trough-trough).
Result: Maximum resultant amplitude.
Destructive: Waves meet in antiphase (peak-trough).
Result: Minimum or zero resultant amplitude.
Path Difference and Interference Conditions
The type of interference observed at a point depends on the path difference – how much further one wave has travelled compared to the other to reach that point. This difference is key to determining whether they arrive in phase or antiphase. Imagine two paths from sources S1 and S2 to a point P. If the path S2P is exactly one wavelength longer than S1P, the wave from S2 arrives having completed one full extra cycle, meaning it is back in phase with the wave from S1, causing constructive interference.
For Constructive Interference: Path difference = (where ) For Destructive Interference: Path difference = (where )
Remember that 'n' starts from 0 for both constructive and destructive interference. Don't confuse the conditions – integer multiples of for constructive, and odd half-multiples of for destructive!
Diffraction: Creating Coherent Sources
Diffraction is the bending or spreading of waves as they pass through an opening or around an obstacle. When a wave (like light) from a single source passes through a narrow slit, it spreads out, effectively creating a new point source. This phenomenon is crucial for creating the coherent sources needed for many interference experiments, such as Young's double-slit.
Diffraction is the spreading of waves.
Occurs when waves pass through apertures or around obstacles.
Creates secondary coherent sources from a single primary source.
Most significant when wavelength is comparable to the obstacle/aperture size.
Young's Double-Slit Experiment
This iconic experiment beautifully demonstrates the wave nature of light. Monochromatic light first passes through a single slit, then through two closely spaced parallel slits. These two slits act as coherent sources, producing an observable interference pattern of alternating bright (constructive) and dark (destructive) fringes on a screen.
Where: = wavelength of light = separation between the two slits = fringe spacing (distance between centres of adjacent bright or dark fringes) = distance from the slits to the screen
This formula is derived using the small angle approximation. For the angles involved in a typical Young's double-slit setup, we assume that sin θ ≈ tan θ ≈ θ (in radians). This is valid because the distance to the screen, D, is usually much larger than the fringe spacing, x. The path difference is approximately a sin θ, and the position on the screen is given by y = D tan θ. Equating these under the approximation leads to the formula.
Diffraction Gratings: Sharper Patterns
A diffraction grating takes the idea of double slits much further. It consists of a very large number of equally spaced parallel slits. This arrangement produces much sharper, brighter interference maxima compared to just two slits, making it ideal for precise measurements and analysis, particularly in spectroscopy where accurate wavelength determination is essential.
Where: = spacing between adjacent slits on the grating = angle of the maximum from the central maximum = order of the maximum ( for central, for first order, etc.) = wavelength of light
An important consideration with diffraction gratings is the maximum number of orders that can be observed. Since the maximum value of sin θ is 1 (for θ = 90°), the grating equation d sin θ = nλ implies that nλ must be less than or equal to d. Therefore, the maximum order, n_max, is the largest integer that is less than or equal to d/λ. Any higher orders are physically impossible to observe.
Composed of many equally spaced parallel slits.
Produces sharper and brighter interference maxima than double slits.
Used for precise wavelength measurements and spectroscopy.
The maximum possible order () for a given wavelength is limited by .
Be careful to distinguish between the 'slit separation' () in Young's experiment and the 'grating spacing' () in the diffraction grating formula. While similar conceptually, they are used in different contexts and formulas.
Worked examples
See the formulas applied — reveal one step at a time, like the exam.
In a Young's double-slit experiment, light of wavelength 600 nm is used. The slits are separated by 0.50 mm, and the screen is placed 2.0 m away. Calculate the fringe spacing observed on the screen.
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Identify known values: , , .
A diffraction grating with 500 lines per mm is illuminated with monochromatic light of wavelength 589 nm. The light is incident normally on the grating. What is the angle of the second-order maximum?
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First, calculate the grating spacing, d. The grating has 500 lines per mm, which is 500,000 lines per metre.
How it all connects
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Glossary
Key terms for this topic — skim now; the Check step will test them.
- coherent
For us to observe a stable, unchanging interference pattern, the interacting waves must be coherent. This means they need to have the exact same frequency and wavelength, and crucially, maintain a constant phase relationship over time.
- destructive interference
Conversely, destructive interference occurs when waves meet exactly out of phase (antiphase), like a crest meeting a trough, leading to a minimum or even zero resultant amplitude.
- path difference
How much further one wave has travelled compared to the other to reach that point.
- Diffraction
Diffraction is the bending or spreading of waves as they pass through an opening or around an obstacle.
- diffraction grating
A diffraction grating takes the idea of double slits much further. It consists of a very large number of equally spaced parallel slits.
- Constructive Interference
For Constructive Interference: Path difference = (where )
Quick check
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Revision flashcards
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Key takeaways
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8.3 Interference.
Interference occurs when waves overlap and their resultant displacement is the sum of the displacement of each wave .
Waves are coherent if they have the same frequency and constant phase difference .
Two-source interference can be demonstrated in water using ripple tanks .
Laser through two slits can also form interference patterns.
For two-source interference fringes to be observed, the sources of wave must be coherent and monochromatic (single wavelength).
Practice — then mark it
The whole point: a real Cambridge question, marked mark-by-mark.
State and explain the effect of this change on the number of bright fringes formed on the screen. A calculation is not required.
Wave X and wave Y superpose to form a resultant wave. On Fig. 3.2, sketch the variation of displacement of the resultant wave with distance from A at the instant of time shown in Fig. 3.1.
Extra simulations & links
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Frequently asked
Checkpoint
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Before you move on: do 9702/22 · Q6(b)(ii) on paper, snap a photo, and get examiner-style feedback on exactly where you win and lose marks.
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