Physics • Year 11 • Module 3 • Lesson 2
Wave Properties and the Wave Equation
Lock in the core vocabulary, the wave equation v = fλ, and the key difference between displacement‑distance and displacement‑time graphs before tackling harder questions.
1. Term–definition match
The definitions below are shuffled. In the right-hand column write the matching term from this list: wave speed, frequency, wavelength, period, amplitude, v = fλ, T = 1/f, displacement‑distance graph, displacement‑time graph, antiphase. 10 marks (1 each)
| # | Definition | Matching term |
|---|---|---|
| 1.1 | The distance a disturbance travels through a medium per second; determined mainly by the medium’s properties. | |
| 1.2 | The number of complete wave cycles per second; unit is hertz (Hz); set by the source. | |
| 1.3 | The distance between two consecutive points in phase on a wave, such as crest to crest; measured in metres. | |
| 1.4 | The time for one complete oscillation; equal to the reciprocal of frequency. | |
| 1.5 | The maximum displacement of a particle from its equilibrium position. | |
| 1.6 | The wave equation linking wave speed, frequency and wavelength; at fixed speed, f and λ are inversely proportional. | |
| 1.7 | The relationship between period and frequency; each is the reciprocal of the other. | |
| 1.8 | A graph that is a snapshot across space at one moment; its horizontal axis gives wavelength. | |
| 1.9 | A graph that shows the motion of one point over time; its horizontal axis gives period. | |
| 1.10 | The phase relationship between two points separated by half a wavelength; they have equal but opposite displacements. |
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 the source frequency doubles while a wave stays in the same medium, its wavelength also doubles. T / F
2.2 Amplitude is the distance from the crest of a wave to the trough directly below it. T / F
2.3 On a displacement-time graph, the horizontal spacing between two crests gives the period of the wave. T / F
2.4 When a sound wave passes from air into water, its frequency changes to match the new medium. T / F
2.5 Two points separated by one full wavelength are in phase — they have the same displacement and the same direction of motion. T / F
2.6 In the wave equation v = fλ, the wave speed v is mainly determined by the source that generates the wave. T / F
3. Fill-in-the-blank paragraph
Use the word bank to complete the passage. Each word or phrase is used once. 8 marks (1 per blank)
Word bank:
amplitude · frequency · halves · hertz · medium · period · source · wavelength
The wave equation v = fλ links wave speed, ___________ and ___________. Frequency is measured in ___________ and is determined by the ___________ of the wave, not the medium through which it travels. When a wave crosses into a different ___________, the frequency stays constant but the speed and wavelength change. If the speed stays fixed and the frequency doubles, the wavelength ___________. The time for one complete oscillation is called the ___________, and it equals 1/f. The maximum displacement from equilibrium is called the ___________; it is not related to the wave’s speed or frequency.
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 horizontal axis represent on a displacement-distance graph, and what does it represent on a displacement-time graph?
4.2 Why does doubling the frequency of a wave in the same medium cause the wavelength to halve?
4.3 What is the phase relationship between two points separated by half a wavelength, and what does this mean for their displacements?
4.4 Why is a higher-frequency wave in the same medium not necessarily a faster wave?
5. Label the wave graph
The displacement-distance graph below shows one complete wave. Write the correct label into boxes A–D from the list: amplitude, crest, wavelength, equilibrium position. 4 marks (1 each)
| Label | Term | Brief explanation (1 sentence) |
|---|---|---|
| A | ||
| B | ||
| C | ||
| D |
Q1 — Term–definition match
1.1 wave speed • 1.2 frequency • 1.3 wavelength • 1.4 period • 1.5 amplitude • 1.6 v = fλ • 1.7 T = 1/f • 1.8 displacement-distance graph • 1.9 displacement-time graph • 1.10 antiphase.
Q2 — True / false with correction
2.1 False. In the same medium, wave speed is approximately fixed. Doubling frequency therefore halves wavelength (since v = fλ must remain constant).
2.2 False. Amplitude is the maximum displacement from the equilibrium position (crest to equilibrium, not crest to trough). Crest-to-trough distance equals twice the amplitude.
2.3 True.
2.4 False. Frequency is set by the source and remains constant when a wave crosses a boundary. Only wave speed and wavelength change in the new medium.
2.5 True.
2.6 False. Wave speed is determined mainly by the medium, not the source. The source determines frequency; the medium determines how fast the disturbance travels.
Q3 — Cloze paragraph
In order: frequency / wavelength / hertz / source / medium / halves / period / amplitude.
Q4.1 — Horizontal axis on wave graphs
On a displacement-distance graph the horizontal axis represents position (metres), so crest-to-crest spacing gives the wavelength. On a displacement-time graph the horizontal axis represents time (seconds), so crest-to-crest spacing gives the period.
Q4.2 — Why doubling frequency halves wavelength
In the same medium, wave speed is approximately constant. From v = fλ, if v is constant and f doubles, then λ = v/f must halve so that the product fλ still equals v.
Q4.3 — Antiphase relationship
Points separated by λ/2 are in antiphase. They have equal but opposite displacements at every instant, and they are moving in opposite directions.
Q4.4 — Higher frequency does not mean faster wave
Wave speed is set by the medium’s properties (tension, density, temperature, etc.), not by the source frequency. In the same medium, a wave with double the frequency travels at the same speed but with half the wavelength.
Q5 — Wave graph labels
A: crest — the maximum positive displacement point on the wave.
B: equilibrium position — the undisturbed (zero displacement) line about which the wave oscillates.
C: amplitude — the maximum displacement from equilibrium to crest (vertical distance from B to A).
D: wavelength — the horizontal distance between two consecutive crests (one complete cycle in space).