What does a piezo-electric crystal do when a p.d. is applied across it?

It changes shape. An alternating p.d. therefore makes it vibrate.

What is the specific acoustic impedance of a medium?

its density × the speed of sound in it. Z = ρc.

What happens at a boundary between two media whose acoustic impedances are very different?

Most of the ultrasound is reflected. The reflected fraction depends on the difference in Z.

Why is a gel used between the transducer and the skin?

to stop almost all the ultrasound being reflected at the skin. A layer of air would reflect nearly all of it.

In I = I₀e^(−μx), what is μ?

the attenuation coefficient. It says how quickly the intensity falls with distance.

Ultrasound scanning · Cambridge A Level Physics revision

In plain words

An ultrasound scan builds a picture out of echoes. A crystal that squeezes itself when a voltage is put across it sends out short bursts of very high-pitched sound, and the same crystal then listens for the reflections from the boundaries inside the body.

5 things to know

A piezo-electric crystal changes shape when a p.d. is applied across it, and generates an e.m.f. when its shape is changed. An alternating p.d. makes it vibrate and send out ultrasound; returning ultrasound makes it vibrate and gives an alternating e.m.f. So one transducer both generates and detects.
Pulses of ultrasound are partly reflected at each boundary between tissues. The time for an echo to return gives the depth of the boundary, and the strength of the echo tells you about the tissues on each side.
Specific acoustic impedance Z = ρc: the density of the medium × the speed of sound in it.
The fraction of the intensity reflected at a boundary is (Z₁ − Z₂)² ÷ (Z₁ + Z₂)². A big difference in Z gives a strong reflection. Almost everything is reflected between air and skin, so a gel is used to fill the gap.
Ultrasound is absorbed as it travels: I = I₀e^(−μx), where μ is the attenuation coefficient and x the distance travelled.

Worked example

Find the fraction of the intensity of ultrasound reflected at a boundary between fat (Z = 1.4 × 10⁶ kg m⁻² s⁻¹) and muscle (Z = 1.7 × 10⁶ kg m⁻² s⁻¹).

(Z₁ − Z₂)² = (0.3 × 10⁶)² = 9.0 × 10¹⁰.
(Z₁ + Z₂)² = (3.1 × 10⁶)² = 9.6 × 10¹².
Fraction reflected = 9.0 × 10¹⁰ ÷ 9.6 × 10¹² = 0.0094, which is just under 1%.

Tips and tricks

The gel is there because its acoustic impedance is close to that of skin. Without it, nearly all the ultrasound would be reflected at the air.
Pulses are used, not a continuous wave, so that each echo can be timed before the next pulse is sent.

5 questions, about 2 minutes.

It lands in your notebook with its questions as flashcards.

Ultrasound scanning: 5 questions and answers

These are the quiz’s questions. Do the quiz first, then come back here for the ones that got you.

What does a piezo-electric crystal do when a p.d. is applied across it?
- It changes shape. (the answer)
- It gets hot.
- It gives out light.
- It becomes magnetic.
An alternating p.d. therefore makes it vibrate.
What is the specific acoustic impedance of a medium?
- its density × the speed of sound in it (the answer)
- its density ÷ the speed of sound in it
- the speed of sound in it ÷ its density
- its density × its volume
Z = ρc.
What happens at a boundary between two media whose acoustic impedances are very different?
- Most of the ultrasound is reflected. (the answer)
- Most of the ultrasound is transmitted.
- All of the ultrasound is absorbed.
- Nothing.
The reflected fraction depends on the difference in Z.
Why is a gel used between the transducer and the skin?
- to stop almost all the ultrasound being reflected at the skin (the answer)
- to cool the skin
- to make the ultrasound louder
- to slow the ultrasound down
A layer of air would reflect nearly all of it.
In I = I₀e^(−μx), what is μ?
- the attenuation coefficient (the answer)
- the density
- the wavelength
- the acoustic impedance
It says how quickly the intensity falls with distance.

5 questions

Tap an answer and you’ll see straight away whether it’s right, and why.

Worksheet

4 questions, 9 marks. Write your answers on paper, then check them.

Ultrasound scanning

Cambridge International AS & A Level Physics 9702 · 9 marks · papermunch.org

Name ______________________________ Date ______________

Find the specific acoustic impedance of water. Its density is 1000 kg/m³ and sound travels through it at 1500 m/s.[2]
Show answerHide answer
1.5 × 10⁶ kg m⁻² s⁻¹.
I got this one
Explain how a piezo-electric transducer generates ultrasound and how it detects it.[3]
Show answerHide answer
To generate: an alternating p.d. is applied across the crystal, which makes it change shape repeatedly, so it vibrates and sends out ultrasound. To detect: the returning ultrasound makes the crystal vibrate, and its changing shape produces an alternating e.m.f. across it.
I got this one
Ultrasound travels 0.020 m through tissue with an attenuation coefficient of 50 m⁻¹. Find the fraction of its intensity that remains.[2]
Show answerHide answer
0.37. e^(−50 × 0.020) = e⁻¹.
I got this one
Explain why a gel is put between the transducer and the skin.[2]
Show answerHide answer
Air and skin have very different acoustic impedances, so almost all the ultrasound would be reflected at the skin. The gel has an impedance close to that of skin, so most of the ultrasound passes into the body.
I got this one

Answers: Ultrasound scanning

1. 1.5 × 10⁶ kg m⁻² s⁻¹.
2. To generate: an alternating p.d. is applied across the crystal, which makes it change shape repeatedly, so it vibrates and sends out ultrasound. To detect: the returning ultrasound makes the crystal vibrate, and its changing shape produces an alternating e.m.f. across it.
3. 0.37. e^(−50 × 0.020) = e⁻¹.
4. Air and skin have very different acoustic impedances, so almost all the ultrasound would be reflected at the skin. The gel has an impedance close to that of skin, so most of the ultrasound passes into the body.