Physics • Year 11 • Module 3 • Lesson 4
Wave Superposition and Interference
Lock in the core vocabulary of superposition, constructive and destructive interference, path difference, and coherence before moving to calculation tasks.
1. Term–definition match
The definitions below are shuffled. In the right-hand column write the matching term from this list: superposition principle, constructive interference, destructive interference, path difference, phase difference, coherence, antiphase, resultant displacement, order (n), interference pattern. 10 marks (1 each)
| # | Definition | Matching term |
|---|---|---|
| 1.1 | The resultant displacement at any point equals the algebraic sum of the displacements of each individual wave at that point. | |
| 1.2 | The wave overlap that occurs when two waves meet exactly in phase; their amplitudes add and the resultant amplitude is larger than either individual amplitude. | |
| 1.3 | The wave overlap that occurs when two waves meet exactly out of phase; their amplitudes partially or completely cancel. | |
| 1.4 | The difference in distance each wave travels from its source to reach the same observation point. | |
| 1.5 | The fraction of a cycle by which two waves are offset at a given point, expressed in degrees or radians. | |
| 1.6 | The property of two sources that have the same frequency and maintain a constant phase relationship, allowing a stable interference pattern to form. | |
| 1.7 | A phase difference of exactly 180°; a crest from one wave aligns with a trough from the other. | |
| 1.8 | The net displacement at a point where two or more waves overlap simultaneously, calculated by algebraically summing the individual displacements. | |
| 1.9 | The non-negative integer in the interference condition equations (nλ or (n+½)λ) that labels successive constructive or destructive regions. | |
| 1.10 | The alternating regions of reinforcement and cancellation produced when two coherent sources emit overlapping waves. |
2. True or false — with correction
Circle T or F. If the statement is false, write the corrected version on the line below it. 12 marks (1 T/F + 1 correction each)
2.1 When two waves overlap, the larger wave replaces the smaller wave. T / F
2.2 After two pulses pass through each other, they continue onward with their original shapes, speeds, and amplitudes unchanged. T / F
2.3 Destructive interference permanently destroys the energy carried by the waves. T / F
2.4 A path difference of 2λ produces constructive interference. T / F
2.5 A path difference of λ/2 produces constructive interference. T / F
2.6 Two independent light bulbs of the same wattage will produce a clear, stable interference pattern because they have approximately the same wavelength. T / F
3. Fill-in-the-blank paragraph
Use the word bank to complete the passage. Each word is used once. 8 marks (1 per blank)
Word bank:
algebraic · antiphase · coherent · constructive · destructive · path difference · redistributed · unchanged
The principle of superposition states that when waves overlap, the resultant displacement equals the ___________ sum of the individual displacements. If two waves meet in phase, they produce ___________ interference, causing the resultant amplitude to increase. If they meet in ___________, they produce ___________ interference, and the amplitude decreases or becomes zero. The key quantity that determines which type of interference occurs at a given point is the ___________ — the difference in distance each wave travels to reach that point. Energy is never destroyed during destructive interference; instead it is ___________ to regions of constructive interference. After waves pass through each other, they continue with their original shapes and amplitudes ___________. A stable interference pattern can only form if the two sources are ___________.
4. Function recall
Answer each question in 1–2 sentences using precise terms from the lesson. 8 marks (2 each)
4.1 What does the path difference tell you about wave interference at a given point?
4.2 Why must sources be coherent for a stable interference pattern to exist?
4.3 What is the function of path difference in deciding whether interference is constructive (nλ) or destructive ((n + ½)λ)?
4.4 Why does destructive interference not violate conservation of energy?
5. Build a concept map
Draw labelled arrows between the six terms below to show how they connect. Each arrow must carry a linking phrase (e.g. “requires”, “determines”, “produces”). Aim for at least 6 labelled arrows. 6 marks (1 per valid labelled arrow)
Supplied terms: superposition principle · path difference · coherent sources · constructive interference · destructive interference · interference pattern.
6. Complete the path-difference table
Fill in the empty cells to complete the relationship between path difference, interference type, and phase relationship. 6 marks (1 per blank cell)
| Path difference | Interference type | Phase relationship |
|---|---|---|
| 0 | ||
| Destructive | Antiphase (180°) | |
| 2λ | ||
| Destructive | Antiphase (540°) | |
| 3λ | ||
| 5λ/2 |
Q1 — Term–definition match
1.1 superposition principle • 1.2 constructive interference • 1.3 destructive interference • 1.4 path difference • 1.5 phase difference • 1.6 coherence • 1.7 antiphase • 1.8 resultant displacement • 1.9 order (n) • 1.10 interference pattern.
Q2 — True / false with correction
2.1 False. When waves overlap, their displacements add algebraically. Neither wave “replaces” the other; the resultant displacement is the sum of both individual displacements.
2.2 True. Waves pass through each other without permanent alteration; original shape, speed, and amplitude are restored after overlap.
2.3 False. Destructive interference does not destroy energy. Energy is redistributed — it shifts from regions of destructive interference to regions of constructive interference. Total energy is conserved.
2.4 True. A path difference of 2λ satisfies nλ (with n = 2), so constructive interference occurs.
2.5 False. A path difference of λ/2 satisfies (n + ½)λ with n = 0, which is the condition for destructive interference, not constructive.
2.6 False. Two independent light bulbs are incoherent: their phases shift randomly relative to each other. Without a constant phase relationship, no stable interference pattern forms, only a uniform average intensity.
Q3 — Cloze paragraph
In order: algebraic / constructive / antiphase / destructive / path difference / redistributed / unchanged / coherent.
Q4.1 — Function of path difference
The path difference tells you the difference in distance each wave has travelled to reach the observation point. Comparing this to the wavelength determines whether the waves arrive in phase (constructive) or antiphase (destructive).
Q4.2 — Why coherence is needed
If sources are not coherent, their phase relationship drifts continuously, so the positions of constructive and destructive interference keep shifting. The pattern blurs to a uniform average, making no distinct bright or dark regions observable.
Q4.3 — Role of path difference in interference conditions
Path difference is compared to the wavelength to classify the interference: if it equals nλ (a whole number of wavelengths), the waves arrive in phase and interfere constructively; if it equals (n + ½)λ, they arrive in antiphase and interfere destructively.
Q4.4 — Energy conservation and destructive interference
Destructive interference produces zero or reduced amplitude only in certain regions. The energy that “disappears” from these regions is redistributed to the regions of constructive interference, where the amplitude is enhanced. The total energy across the entire pattern is conserved.
Q5 — Sample concept map
Accept any valid arrows. Exemplars:
- superposition principle — governs → constructive interference
- superposition principle — governs → destructive interference
- path difference — determines whether produces → constructive interference
- path difference — determines whether produces → destructive interference
- coherent sources — required for stable → interference pattern
- constructive & destructive interference — combine to form → interference pattern
Award 1 mark per valid labelled arrow (minimum 6 marked).
Q6 — Path-difference table
Row 1: Constructive / In phase (0°). Row 2: path difference = λ/2. Row 3: Constructive / In phase (720°). Row 4: path difference = 3λ/2. Row 5: Constructive / In phase (1080°). Row 6: Destructive / Antiphase (900°).
Accept equivalent expressions: e.g. “in phase” for 360° multiples; “antiphase” or “out of phase by 180°” for odd multiples of 180°.