The shape of the lesson
By the end of the lesson, learners can
- Match, or reflect: Set the acoustic impedance of two media and watch how much of the pulse echoes back.
- Transducer, impedance, attenuation: The marks come from a few clear ideas.
- Ultrasound: Z = ρc; Iᵣ/I₀ = (Z₁ − Z₂)²/(Z₁ + Z₂)²; depth d = ½ct.
- X-rays: hfₘₐₓ = eV; attenuation I = I₀e⁻μᵛ; half-value thickness ln2/μ.
- PET: β⁺ tracer; e⁻ + e⁺ → 2γ of 0.511 MeV, opposite directions; coincidence gives a line of response.
One picture every idea returns to
A piezoelectric transducer both produces and detects ultrasound. A pulse partly reflects at every boundary where the acoustic impedance Z = ρc changes; the fraction reflected is the intensity reflection coefficient Iᵣ/I₀ = (Z₁ − Z₂)² / (Z₁ + Z₂)². Timing the echoes gives the depth, and a coupling gel removes the air gap that would otherwise reflect almost everything.
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, Listening for the echo.. Send a pulse of sound too high to hear into the body, and time the echoes that bounce back from each boundary. Put the figure on the board: it is the one picture every idea in the lesson returns to. | Whole class, then pairs |
| 5 to 17 min | Teach and check: Match, or reflect | Set the acoustic impedance of two media and watch how much of the pulse echoes back. Project tab 1 of the lab (Ultrasound) and let a student drive it while the class predicts. | Whole class, then pairs |
| 17 to 30 min | Teach and check: Transducer, impedance, attenuation | The marks come from a few clear ideas. | Think-Pair-Share |
| 30 to 43 min | Check and plenary | The quick-check questions from the student lesson, answered on mini whiteboards one at a time; re-teach the one most get wrong, then a random call on the last. | Individual, then whole class |
| 43 to 45 min | Exit and homework | Set the worksheet below (4 questions, 30 marks) from the topic practice set. 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 Transducer, impedance, attenuation, 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.
Think-Pair-Share
Pose the question, give thirty seconds of silent thinking, then a minute to compare with a partner before a few pairs share with the class. The silent minute is the part that cannot be cut.
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 |
|---|---|
| The reflection coefficient depends on the difference in impedance, not the impedance itself; matched media (small Z₁ − Z₂) give almost no echo. | When timing an echo to find depth, remember the pulse travels there and back, so d = ½ct. The coupling gel is needed because a thin layer of air between the probe and skin would reflect about 99.9% of the ultrasound. |
Production and use of ultrasound: topic worksheet
4 questions, 30 marks. Written in the style of the papers; no past paper question is reproduced. These questions cover the whole topic, so sibling lessons share them.
Soft tissue has density 1060 kg m⁻³ and the speed of sound in it is 1540 m s⁻¹.
(a) State what is meant by the specific acoustic impedance of a medium. [1]
(b) Calculate the acoustic impedance of soft tissue. [2]
(c) Explain how a piezoelectric transducer both generates and detects ultrasound. [3]
(d) State why ultrasound, rather than audible sound, is used for imaging. [1]
At a boundary, the intensity reflection coefficient is Iᵣ/I₀ = (Z₁ − Z₂)²/(Z₁ + Z₂)². Impedances (×10⁶ kg m⁻² s⁻¹): fat 1.38, muscle 1.70, air 0.0004.
(a) Calculate the fraction of intensity reflected at a fat-muscle boundary. [2]
(b) Calculate the fraction reflected at a tissue (Z = 1.63)-air boundary. [2]
(c) Use your answers to explain why a coupling gel is used. [2]
(d) State why little of the ultrasound is reflected at a fat-muscle boundary. [2]
In an A-scan, an echo from a boundary returns 40 µs after the pulse is sent. The speed of sound in the tissue is 1540 m s⁻¹.
(a) Calculate the depth of the boundary below the probe. [3]
(b) Explain why the factor of one half appears in your calculation. [2]
(c) State what the size of an echo indicates. [1]
A clinic must choose an imaging method for three cases.
(a) State which of the three techniques use ionising radiation, and which does not. [2]
(b) Suggest the best method to monitor a developing fetus, with a reason. [2]
(c) Suggest the best method to check for a bone fracture, with a reason. [2]
(d) Suggest the best method to find an area of unusually high metabolic activity, with a reason. [3]
Answer key and marking notes
- (a)Z = ρc, the product of density and speed of sound in the medium ✓
- (b)Z = 1060 × 1540 ✓ = 1.6 × 10⁶ kg m⁻² s⁻¹ ✓
- (c)An alternating p.d. makes the piezoelectric crystal vibrate and emit ultrasound ✓; returning ultrasound deforms the crystal ✓, generating an e.m.f. that is detected ✓
- (d)Its short wavelength gives better resolution (smaller detail can be imaged) ✓
- (a)(1.38 − 1.70)²/(1.38 + 1.70)² = 0.1024/9.486 ✓ = 0.011 (1.1%) ✓
- (b)(1.63 − 0.0004)²/(1.63 + 0.0004)² ✓ ≈ 0.999 (99.9%) ✓
- (c)An air gap reflects almost all the ultrasound ✓; the gel (matched to tissue) excludes the air so the pulse can enter and echoes return ✓
- (d)Fat and muscle have nearly equal impedances ✓, so Z₁ − Z₂ is small and little is reflected (most is transmitted) ✓
- (a)d = ½ct = ½ × 1540 × 40 × 10⁻⁶ ✓✓ = 0.031 m = 3.1 cm ✓
- (b)The pulse travels to the boundary and back ✓, so the measured time covers twice the depth ✓
- (c)The size of the impedance mismatch at that boundary (a bigger mismatch gives a larger echo) ✓
- (a)X-rays/CT and PET use ionising radiation ✓; ultrasound does not ✓
- (b)Ultrasound ✓; it is non-ionising and so safe for the fetus, and gives real-time soft-tissue images ✓
- (c)X-ray ✓; bone has a high attenuation coefficient, giving strong contrast against soft tissue ✓
- (d)PET ✓; a tracer that follows metabolism concentrates in active tissue ✓, and the annihilation gamma pairs map where it gathers ✓
The lesson's own checks as a quiz
The quick-check and exam-style questions from the student lesson, printable with the key.
A piezoelectric transducer produces ultrasound because the crystal:
- Avibrates when an alternating p.d. is applied across it
- Bheats up and glows
- Cemits electrons when struck by light
- Dbecomes radioactive
The specific acoustic impedance of a medium is given by:
- AZ = ρc
- BZ = ρ/c
- CZ = c/ρ
- DZ = ρc²
The fraction of ultrasound intensity reflected at a boundary is largest when the two media have:
- Avery different acoustic impedances
- Bequal acoustic impedances
- Cthe same density
- Dthe same colour
A coupling gel is smeared between the probe and the skin in order to:
- Aexclude the air gap, which would otherwise reflect almost all the ultrasound
- Bcool the probe down
- Cmake the ultrasound travel faster
- Dblock the echoes
Quiz key
A piezoelectric crystal changes shape with applied p.d.; an alternating p.d. at its natural frequency makes it vibrate strongly and emit ultrasound. The reverse effect lets it detect echoes.
Acoustic impedance Z = ρc, the product of the density ρ and the speed of sound c in the medium.
Iᵣ/I₀ = (Z₁ − Z₂)²/(Z₁ + Z₂)² is largest when the impedance difference is largest; matched impedances reflect almost nothing.
Air has a tiny acoustic impedance, so a tissue-air boundary reflects about 99.9%. The gel matches the skin's impedance, letting the pulse enter and the echoes return.
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.