Physics • Year 11 • Module 3 • Lesson 3
Wave Intensity and the Inverse Square Law
Lock in the core vocabulary, the inverse square law, and the amplitude–intensity relationship before tackling harder problems.
1. Term–definition match
The definitions below are shuffled. In the right-hand column write the matching term from this list: intensity, inverse square law, amplitude, power, point source, wavefront, spherical spreading, watts per square metre. 8 marks (1 each)
| # | Definition | Matching term |
|---|---|---|
| 1.1 | The power delivered per unit area of a wave; symbol I; SI unit W/m². | |
| 1.2 | The relationship I ∝ 1/r² showing how intensity falls with distance from a point source. | |
| 1.3 | The maximum displacement of a particle from its equilibrium position; related to intensity by I ∝ A². | |
| 1.4 | Energy transferred per unit time; measured in watts (W). | |
| 1.5 | A small source that radiates energy equally in all directions, so wavefronts are spherical. | |
| 1.6 | A surface connecting all points in a wave that have the same phase at a given instant. | |
| 1.7 | The geometric process by which energy from a point source is distributed over an area that grows with r². | |
| 1.8 | The SI unit of intensity: one watt per square metre. |
2. True or false — with correction
Circle T or F for each statement. If the statement is false, write the corrected version on the line below it. 12 marks (1 T/F + 1 correction each)
2.1 If you double the distance from a point source, the intensity of the wave halves. T / F
2.2 The inverse square law applies to both sound waves and light waves from a point source. T / F
2.3 Doubling the amplitude of a wave doubles its intensity. T / F
2.4 The inverse square law is a consequence of energy conservation applied to expanding wavefronts in three-dimensional space. T / F
2.5 A laser pointer obeys the inverse square law in the same way as a small light bulb. T / F
2.6 If distance triples from a point source, intensity becomes one ninth of the original. 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:
amplitude · area · conservation · four · geometric · intensity · squared · point source
___________ is defined as the power of a wave per unit ___________, measured in W/m². For a ___________ radiating energy equally in all directions, the energy spreads over an ever-growing spherical wavefront. The fall in intensity with distance is a ___________ consequence of energy spreading in three-dimensional space—it follows from ___________ of energy. Because the surface area of a sphere grows with the ___________ of the radius, doubling the distance gives ___________ times the area, so intensity falls to one quarter. Separately, intensity also depends on ___________ squared: doubling the amplitude of a wave quadruples its intensity.
4. Formula and proportion recall
Answer each question using precise physics terms from the lesson. 8 marks (2 each)
4.1 Write the two proportional relationships that summarise this lesson’s key formulas. State what each symbol represents.
4.2 Write the ratio form of the inverse square law used when comparing intensities at two different distances.
4.3 Complete the table: fill in the “Intensity change” column.
| Distance change | Intensity change |
|---|---|
| Distance doubles | |
| Distance triples | |
| Distance halves |
4.4 Complete the table: fill in the “Intensity change” column.
| Amplitude change | Intensity change |
|---|---|
| Amplitude doubles | |
| Amplitude triples | |
| Amplitude halves |
5. Build a concept map
Draw labelled arrows between the six terms below to show how they are related. Each arrow must carry a linking phrase (e.g. “is proportional to”, “causes”, “is measured in”). Aim for at least 6 labelled arrows. 6 marks (1 per valid labelled arrow)
Supplied terms: intensity · distance from source · amplitude · wavefront area · source power · inverse square law.
Q1 — Term–definition match
1.1 intensity • 1.2 inverse square law • 1.3 amplitude • 1.4 power • 1.5 point source • 1.6 wavefront • 1.7 spherical spreading • 1.8 watts per square metre.
Marking criteria: 1 mark per correct match. No part marks within each item.
Q2 — True / false with correction
2.1 False. Doubling distance reduces intensity to one quarter (not one half), because intensity is proportional to 1/r² and distance is squared. 1 mark for F; 1 mark for correct explanation (must mention squaring).
2.2 True. Both sound and light from a small source obey I ∝ 1/r² because the same geometric spreading argument applies to all waves from a point source. 1 mark for T only (no correction needed).
2.3 False. Doubling amplitude quadruples intensity because I ∝ A²; if A × 2 then I × 2² = 4. 1 mark for F; 1 mark for correct relationship with squaring shown.
2.4 True. The inverse square law is a direct consequence of energy spreading over an area that grows with r² in three-dimensional space, which itself follows from energy conservation in the absence of absorption. 1 mark for T only.
2.5 False. A laser pointer does not obey the inverse square law in the same way because the light is collimated—it travels in a narrow, nearly parallel beam rather than spreading spherically. Intensity drops far more slowly with distance than for a point source. 1 mark for F; 1 mark for correct explanation (collimated / does not spread spherically).
2.6 True. Tripling distance means r × 3, so intensity changes by 1/3² = 1/9. 1 mark for T only.
Q3 — Cloze paragraph (8 marks, 1 per blank)
In order: Intensity / area / point source / geometric / conservation / squared / four / amplitude.
Marking criteria: 1 mark per correct blank. Accept minor spelling variants.
Q4 — Formula and proportion recall
4.1 I ∝ 1/r² (where I = intensity, r = distance from source) and I ∝ A² (where A = amplitude). 1 mark for each correct proportionality with symbol explanation (2 marks total).
4.2 I⊂1⁄I⊂2 = r⊂2²⁄r⊂1². 1 mark for the correct ratio form; 1 mark for correct placement (intensities inverted relative to distances).
4.3 Distance doubles → 1/4 intensity; distance triples → 1/9 intensity; distance halves → 4× intensity. 1 mark for all three correct (0 if any error; or 1 mark for 2 of 3).
4.4 Amplitude doubles → 4× intensity; amplitude triples → 9× intensity; amplitude halves → 1/4 intensity. 1 mark for all three correct (as above).
Q5 — Sample concept map (6 marks, 1 per valid labelled arrow)
Accept any valid arrows including:
- distance from source — determines → wavefront area
- distance from source — is described by → inverse square law
- wavefront area — determines → intensity
- source power — is spread over → wavefront area
- amplitude — squared gives → intensity
- inverse square law — predicts → intensity
Award 1 mark per valid labelled arrow (minimum 6, maximum 6 marked). The linking phrase must be present and logically correct. Accept reasonable alternatives (e.g. “is inversely proportional to the square of” for distance–intensity link).