The shape of the lesson
By the end of the lesson, learners can
- Tie the three together: Adjust the frequency and wavelength and watch the wave speed that results.
- One equation, three rearrangements: Knowing any two of speed, frequency and wavelength gives you the third.
One picture every idea returns to
The wave speed equals the frequency multiplied by the wavelength: v = f times wavelength. At a fixed speed, raising the frequency shortens the wavelength, and lowering it lengthens the wavelength.
Forty-five minutes, phase by phase
| Time | Phase | What happens in the room | Grouping |
|---|---|---|---|
| 0 to 5 min | Hook: predict | Open with the question in the title, Speed, frequency, wavelength.. Every wave obeys one tidy rule that ties together how fast it moves, how often it wiggles, and how long each wiggle is. | Whole class, then pairs |
| 5 to 17 min | Teach and check: Tie the three together | Adjust the frequency and wavelength and watch the wave speed that results. Project tab 2 of the lab (Wave equation) and let a student drive it while the class predicts. | Whole class, then pairs |
| 17 to 30 min | Teach and check: One equation, three rearrangements | Knowing any two of speed, frequency and wavelength gives you the third. Model the worked example Worked example on the board, one line at a time. | Anticipation / Reaction Guide |
| 30 to 36 min | Check | The four Stage 1 questions from the student lesson, answered on mini whiteboards or by show of fingers. Re-teach the one most get wrong. | Individual, then whole class |
| 36 to 43 min | Plenary | The exam-style questions from Stage 2, one at a time: thirty seconds alone, then a random call. The feedback lines in the key give the examiner's wording. | Individual, random call |
| 43 to 45 min | Exit and homework | Set the worksheet below (5 questions, 20 marks). Learners self-assess against the objectives before they leave. | Individual |
Protect the parts that carry the learning
The sequence carries about fifty minutes of material, so the lab is driven by one student while the class predicts rather than explored freely. Times are a guide.
Protected: the check at 30 minutes. It is the only individual read on whether the key idea landed, and it is not cut.
Cut first if the build overruns: the last check in One equation, three rearrangements, never the check or the plenary.
In a 60 minute block: run worksheet questions 1 to 3 in class as a Rally Coach set and model both the hardest worked example and its check live.
Anticipation / Reaction Guide
Before the lesson, students mark five statements true or false. After the teaching they mark them again and justify any change of mind in one sentence each. The statements come from the examiner traps below.
The full structure, with its variations and the other twelve, is on the cooperative-learning page.
What to head off, and how
| Trap learners fall into | Teaching move that pre-empts it |
|---|---|
| Keep the units consistent and rearrange with care. | To find wavelength, divide speed by frequency; to find frequency, divide speed by wavelength. Mixing these up is the most common slip. |
The wave equation (v = fλ): worksheet
5 questions, 20 marks. Written in the style of the papers; no past paper question is reproduced.
A domestic microwave oven uses electromagnetic waves of frequency 2.45 GHz to heat food. Electromagnetic waves travel at 3.0 × 10⁸ m/s.
Calculate the wavelength of these microwaves in metres.
A sound wave travelling through water has a wavelength of 75 cm. The speed of sound in water is 1500 m/s.
Calculate the frequency of the wave. Give your final answer in kHz.
A student claims that the wave equation v = fλ can only be used for sound waves, because sound is the type of wave they encounter most often in everyday life.
Explain why the student is mistaken. In your answer, you must refer to at least two specific types of wave other than sound, and state a typical value for the speed of each.
A laboratory laser produces red light of wavelength 633 nm. Light travels through air at approximately 3.0 × 10⁸ m/s.
(a) Express the wavelength 633 nm in metres, in standard form. [1] (b) Calculate the frequency of this light. [2] (c) Calculate the period of one oscillation of this light wave. [2]Two transverse waves, A and B, travel along the same stretched rope. They have the same speed. The wavelength of Wave A is three times the wavelength of Wave B.
(a) State and explain how the frequency of Wave A compares with the frequency of Wave B. [2] (b) Wave B has a frequency of 6.0 Hz. Calculate the frequency of Wave A. [2]Answer key and marking notes
Convert the frequency first:
1 GHz = 10⁹ Hz f = 2.45 GHz = 2.45 × 10⁹ HzRearrange:
v = fλ → λ = v ÷ fSubstitute:
λ = (3.0 × 10⁸) ÷ (2.45 × 10⁹) λ = 0.122 mλ = 0.12 m (2 s.f.)
About 12 cm. That is why microwave ovens are roughly that size inside, and why metal mesh on the door (with holes much smaller than 12 cm) blocks the waves but lets you see through.
Convert wavelength to metres (matching v):
λ = 75 cm = 0.75 mRearrange:
v = fλ → f = v ÷ λSubstitute:
f = 1500 ÷ 0.75 f = 2000 HzConvert to kHz (as the question asked):
1 kHz = 1000 Hzf = 2.0 kHz
Two conversions in one question. The trap is to skip the cm-to-m step and substitute 75 directly. The other trap is to leave the answer in Hz when the question asked for kHz. Both lose marks.
- Light (and all EM waves) in a vacuum: v ≈ 3 × 10⁸ m/s
- Water waves in a ripple tank: v of the order 0.1 to 1 m/s
(a) Convert nm to m
1 nm = 10⁻⁹ m λ = 633 × 10⁻⁹ mλ = 6.33 × 10⁻⁷ m
(b) Frequency
f = v ÷ λ f = (3.0 × 10⁸) ÷ (6.33 × 10⁻⁷)f = 4.74 × 10¹⁴ Hz
(c) Period
T = 1 ÷ f T = 1 ÷ (4.74 × 10¹⁴)T = 2.11 × 10⁻¹⁵ s
Standard form is mandatory for very small numbers. Three prefixes to memorise for waves: n = 10⁻⁹ (nm for light), μ = 10⁻⁶ (sometimes for IR), p = 10⁻¹² (rarely). For frequency it is k = 10³, M = 10⁶, G = 10⁹.
(a) Compare frequencies
Same speed means: v = fAλA = fBλB
If λA = 3 λB, then:
fA × 3λB = fB × λB fA = fB ÷ 3Wave A has one-third the frequency of Wave B
Because at fixed speed, f and λ are inversely proportional. Triple the wavelength means one-third the frequency.
(b) Calculate frequency of Wave A
fA = 6.0 ÷ 3fA = 2.0 Hz
When two quantities are inversely proportional at a fixed third quantity, multiplying one by a factor means dividing the other by the same factor. A reasoning shortcut worth practising.
3 multiple-choice questions on this lesson
From the topic question bank. Assign them in the app for a marked score in your gradebook, or run the topic as a class game.
A wave has a frequency of 50 Hz and a wavelength of 4.0 m. What is its speed?
- A0.08 m/s
- B12.5 m/s
- C54 m/s
- D200 m/s
A sound wave travels at 340 m/s and has a wavelength of 2.0 m. What is its frequency?
- A0.0059 Hz
- B170 Hz
- C338 Hz
- D680 Hz
A wave travels at 12 m/s with a frequency of 3.0 Hz. What is its wavelength?
- A0.25 m
- B4.0 m
- C9.0 m
- D36 m
Quiz key
v = fλ = 50 × 4.0 = 200 m/s. Option B divides the wrong way (f ÷ λ); C adds the numbers.
f = v ÷ λ = 340 ÷ 2.0 = 170 Hz. Option D multiplies instead of dividing; C subtracts.
λ = v ÷ f = 12 ÷ 3.0 = 4.0 m. Option A inverts the fraction; D multiplies.
What to project
The student lesson embeds these tabs. Open them full screen on the projector; every slider has a drag handle on the stage.
Slides for this lesson
A projectable deck for every pack is on the way. Until then, present the student lesson full screen: its sections, figure and lab tabs follow the same order as the plan above.