The shape of the lesson
By the end of the lesson, learners can
- Stretch the wave, time the wave: Adjust the frequency and wavelength and watch the wave travel; the read-out confirms v = fλ at every setting.
- The vocabulary of a wave: Each term has a precise meaning worth memorising.
- Reading a CRO trace: The cathode-ray oscilloscope turns a signal into a picture you can measure.
- Wave equation: v = fλ.
- Phase: one wavelength is 360°.
- Intensity: proportional to amplitude squared.
One picture every idea returns to
A progressive wave transfers energy without transferring matter. It is described by its displacement, amplitude, wavelength, period and frequency, with phase difference comparing the motion of two points. The speed, frequency and wavelength obey v = fλ, and the intensity is proportional to the square of the amplitude.
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, Energy without matter.. A wave carries energy from place to place while the medium itself only oscillates about a fixed point. Put the figure on the board: it is the one picture every idea in the lesson returns to. | Whole class, then pairs |
| 5 to 13 min | Teach and check: Stretch the wave, time the wave | Adjust the frequency and wavelength and watch the wave travel; the read-out confirms v = fλ at every setting. Project tab 1 of the lab (Progressive waves) and let a student drive it while the class predicts. | Whole class, then pairs |
| 13 to 21 min | Teach and check: The vocabulary of a wave | Each term has a precise meaning worth memorising. | Pairs |
| 21 to 30 min | Teach and check: Reading a CRO trace | The cathode-ray oscilloscope turns a signal into a picture you can measure. | Corners |
| 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 (6 questions, 14 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 Reading a CRO trace, 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.
Corners
Put one answer or viewpoint in each corner of the room. Students move to the corner they agree with, justify the choice to a partner there, then hear one voice from each corner before the reveal.
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 amplitude and intensity distinct: intensity goes as amplitude squared, so halving the amplitude quarters the intensity. | When using v = fλ, make sure the wavelength is in metres and the frequency in hertz. A wave transfers energy, not matter: the particles of the medium do not travel with the wave. |
Progressive waves: worksheet
6 questions, 14 marks. Written in the style of the papers; no past paper question is reproduced.
Define the amplitude and the wavelength of a wave.
A wave has a frequency of 25 Hz and a wavelength of 0.40 m. Find its speed.
A radio station broadcasts at 100 MHz. Taking the speed of radio waves as 3.0 × 10⁸ m s⁻¹, find the wavelength.
Two points on a wave have a phase difference of 180°. How far apart are they, as a fraction of a wavelength?
On a CRO the time-base is 5.0 ms per division and one complete cycle occupies 4.0 divisions. Find the frequency of the signal.
The amplitude of a wave is tripled with no other change. State the effect on its intensity.
Answer key and marking notes
- Amplitude is the maximum displacement from the equilibrium position ✓
- Wavelength is the distance for one complete cycle of the wave ✓
- v = fλ = 25 × 0.40 ✓
- v = 10 m s⁻¹ ✓
- λ = v / f = (3.0 × 10⁸) / (100 × 10⁶) ✓
- λ = 3.0 m ✓
- 180° is half a cycle ✓
- So the points are half a wavelength (λ/2) apart ✓
- Period = 4.0 × 5.0 ms = 20 ms = 0.020 s ✓
- f = 1 / T = 1 / 0.020 = 50 Hz ✓
- Intensity is proportional to amplitude squared ✓
- So it becomes 3² = 9 times as great ✓
10 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.
The wave equation is:
- Av = fλ
- Bv = f/λ
- Cv = λ/f
- Df = vλ
A wave of frequency 20 Hz has a wavelength of 1.5 m. Its speed is:
- A13 m s⁻¹
- B0.075 m s⁻¹
- C30 m s⁻¹
- D21.5 m s⁻¹
The amplitude of a wave is the:
- Adistance for one cycle
- Bmaximum displacement from equilibrium
- Ctime for one cycle
- Dnumber of cycles per second
A wave has a period of 0.025 s. Its frequency is:
- A25 Hz
- B0.025 Hz
- C400 Hz
- D40 Hz
Two points half a wavelength apart on a wave have a phase difference of:
- A180°
- B360°
- C90°
- D0°
The intensity of a wave is proportional to the:
- Aamplitude
- Bwavelength
- Csquare of the amplitude
- Dperiod
A sound wave travels at 340 m s⁻¹ with a frequency of 170 Hz. Its wavelength is:
- A0.50 m
- B2.0 m
- C510 m
- D58 m
On a CRO the time-base is 1.0 ms per division; one cycle spans 8.0 divisions. The frequency is:
- A8 Hz
- B1000 Hz
- C80 Hz
- D125 Hz
A progressive wave transfers:
- Aenergy without transferring matter
- Bmatter without energy
- Cboth matter and energy along its length
- Dneither
If the amplitude of a wave is halved, its intensity becomes:
- Aa half
- Bdouble
- Ca quarter
- Dunchanged
Quiz key
Speed = frequency × wavelength.
v = fλ = 20 × 1.5 = 30 m s⁻¹.
Amplitude is the maximum displacement from the rest position.
f = 1/T = 1/0.025 = 40 Hz.
Half a wavelength is half a cycle, a phase difference of 180°.
Intensity ∝ amplitude².
λ = v/f = 340/170 = 2.0 m.
T = 8.0 ms = 0.008 s; f = 1/T = 125 Hz.
A progressive wave carries energy; the medium only oscillates.
Intensity ∝ amplitude², so halving the amplitude quarters the intensity.
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.