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.

Build · Vocab & Recall

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)

#DefinitionMatching term
1.1The distance a disturbance travels through a medium per second; determined mainly by the medium’s properties.
1.2The number of complete wave cycles per second; unit is hertz (Hz); set by the source.
1.3The distance between two consecutive points in phase on a wave, such as crest to crest; measured in metres.
1.4The time for one complete oscillation; equal to the reciprocal of frequency.
1.5The maximum displacement of a particle from its equilibrium position.
1.6The wave equation linking wave speed, frequency and wavelength; at fixed speed, f and λ are inversely proportional.
1.7The relationship between period and frequency; each is the reciprocal of the other.
1.8A graph that is a snapshot across space at one moment; its horizontal axis gives wavelength.
1.9A graph that shows the motion of one point over time; its horizontal axis gives period.
1.10The phase relationship between two points separated by half a wavelength; they have equal but opposite displacements.
Stuck? Revisit the Key Terms panel and the Wave Graphs card in the lesson.

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

Stuck? Revisit the Misconceptions box and the Medium Sets the Speed card in the lesson.

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.

Stuck? Revisit the Key Terms panel and the Wave Equation card in the lesson.

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?

Stuck? Revisit the Wave Equation card and the Medium Sets the Speed card in the lesson.

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)

distance (m) displacement A B C D
Figure 5. Displacement-distance snapshot. Choose from: amplitude, crest, wavelength, equilibrium position.
LabelTermBrief explanation (1 sentence)
A
B
C
D
Stuck? Revisit the Reading Wave Graphs card and the inline SVG wave comparison in the lesson.
Answers — Do not peek before attempting

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).