Ultrasound imaging

CIE A-Level Physics· 9702/22, 9702/42· 10 min read

1. Production and Detection of Ultrasound★★☆☆☆⏱ 3 min

Ultrasound is defined as sound with frequency above 20 kHz, the upper limit of human hearing. For medical imaging, frequencies between 1 MHz and 10 MHz are typically used: higher frequencies give better resolution but are absorbed more quickly, so cannot penetrate as deep.

📘 Definition

Piezoelectric Effect

An effect observed in certain crystals (e.g. quartz) where: (1) mechanical deformation of the crystal induces an e.m.f. across it, and (2) an applied alternating e.m.f. causes mechanical deformation/vibration of the crystal.

Example:

An applied a.c. voltage of 2 MHz will make the crystal vibrate at 2 MHz, emitting 2 MHz ultrasound waves.

📐 Worked Example

Explain why a single piezoelectric crystal can be used for both production and detection of ultrasound.

1
For production: When an alternating voltage matching the required ultrasound frequency is applied across the crystal, it vibrates at that frequency, emitting ultrasound waves.
2
For detection: When reflected ultrasound waves hit the crystal, they cause the crystal to deform mechanically.
3
This deformation induces an alternating e.m.f. across the crystal, matching the frequency of the reflected wave. This signal can be processed by electronic equipment.

2. Acoustic Impedance and Reflection★★★☆☆⏱ 4 min

When an ultrasound beam reaches a boundary between two different media, part of the intensity is reflected and part is transmitted. The proportion reflected depends on the difference in acoustic impedance of the two media.

📘 Definition

Acoustic Impedance

Z

The product of the density ( $ρ$ ) of the medium and the speed ( $c$ ) of ultrasound in the medium: $Z = ρ c$ . Units are kg m⁻² s⁻¹.

Example:

Z for air is ~4 × 10² kg m⁻² s⁻¹, and Z for soft tissue/skin is ~1.7 × 10⁶ kg m⁻² s⁻¹.

The intensity reflection coefficient $α$ is given by the formula:

\alpha = \frac{I_r}{I_0} = \frac{(Z_2 - Z_1)^2}{(Z_2 + Z_1)^2}

📐 Worked Example

Calculate the fraction of incident ultrasound intensity reflected at an air-skin boundary. $Z_{ai r} = 4.3 \times 1 0^{2}$ kg m⁻² s⁻¹, $Z_{s k in} = 1.7 \times 1 0^{6}$ kg m⁻² s⁻¹. Comment on your result.

1
Substitute values into the formula for $α$ :
2
$\alpha = \frac{(1.7 \times 10^6 - 4.3 \times 10^2)^2}{(1.7 \times 10^6 + 4.3 \times 10^2)^2}$
3
Since $Z_{ai r} << Z_{s k in}$ , the difference and sum are approximately equal to $Z_{s k in}$ , so $α \approx 1.0$ (calculated value ≈ 0.999).
4
Comment: Almost all incident intensity is reflected at an air-skin boundary, which is why we use ultrasound gel for impedance matching, to eliminate the air gap between transducer and skin.

3. Ultrasound Scanning Techniques★★☆☆☆⏱ 2 min

Two main scanning techniques are used for diagnostic imaging:

A-scan (Amplitude scan): A single transducer sends a pulse along one line into the body. Reflected pulses are displayed as peaks on an oscilloscope. The time delay of the peak gives the depth of the boundary, and peak amplitude gives the reflection intensity. Used for simple measurements like eye lens thickness.
B-scan (Brightness scan): A moving transducer or array of transducers sends pulses along multiple lines. Each reflected pulse is converted to a dot on a screen, where brightness corresponds to reflection intensity. Combining all lines produces a 2D real-time image. This is the standard technique for prenatal imaging.

📐 Worked Example

State one use each for an A-scan and a B-scan, and one key difference between them.

1
Difference: An A-scan produces a 1-dimensional plot of amplitude against depth, while a B-scan produces a full 2-dimensional image of internal body structures.
2
Use of A-scan: Measuring the size of the eye or detecting the depth of a brain tumour.
3
Use of B-scan: Producing a real-time image of a fetus during pregnancy, or imaging gallstones or other organ abnormalities.

4. Advantages and Limitations★★☆☆☆⏱ 1 min

Advantages: Non-ionising (no DNA damage, safe for repeated use and for pregnant patients), produces real-time moving images, lower cost than CT or MRI, portable.
Limitations: Cannot penetrate bone or air-filled organs (e.g. lungs), higher frequency ultrasound has poor depth penetration, lower resolution than CT or MRI for deep structures.

5. Common Pitfalls

Wrong move:

Claiming ultrasound is electromagnetic radiation.

Why:

Ultrasound is a mechanical pressure wave, it requires a medium to travel and cannot propagate through a vacuum.

Correct move:

Always classify ultrasound as a mechanical longitudinal wave with frequency above 20 kHz.

Wrong move:

Forgetting to square the terms in the intensity reflection coefficient formula.

Why:

$α$ is a ratio of intensities, and intensity is proportional to the square of amplitude, so the difference in impedance must be squared.

Correct move:

Memorize $α = \frac{( Z _{2} - Z _{1} ) ^{2}}{( Z _{2} + Z _{1} ) ^{2}}$ , always check your result is between 0 and 1.

Wrong move:

Stating the purpose of ultrasound gel is to lubricate the skin.

Why:

Lubrication is a secondary effect; the key medical purpose is impedance matching.

Correct move:

Explain that gel has a similar acoustic impedance to skin, which eliminates the air gap between transducer and skin, so most ultrasound is transmitted into the body instead of being reflected.

Wrong move:

Confusing A-scan and B-scan, claiming A-scans produce 2D images.

Why:

A-scans only measure along one line, the 'A' stands for Amplitude not 2D Array.

Correct move:

Remember: A = Amplitude (1D), B = Brightness (2D).

6. Quick Reference Cheatsheet

Term	Key Formula/Info	Exam Note
Ultrasound	f > 20 kHz, 1-10 MHz medical	Mechanical longitudinal wave
Acoustic impedance	$Z = ρ c$	Unit: kg m⁻² s⁻¹
Reflection coefficient	$α = \frac{( Z _{2} - Z _{1} ) ^{2}}{( Z _{2} + Z _{1} ) ^{2}}$	$0 \leq α \leq 1$
A-scan	1D amplitude scan	Measures depth of boundaries
B-scan	2D brightness image	Real-time imaging
Ultrasound gel	Impedance matching	Removes air gap between transducer and skin

When this came up on past exams

AI-estimated based on syllabus patterns — cross-check with official past papers for accuracy. Use only as revision-focus signals.

2023 · 4
Acoustic impedance calculation
2022 · 2
A-scan vs B-scan comparison
2021 · 2
Purpose of ultrasound gel

Going deeper

syllabusCIE 9702 Medical Imaging Syllabus

What's Next

Ultrasound imaging is a core application of wave physics in medicine, and builds on your understanding of wave interactions with different media. This knowledge will help you when learning how other imaging techniques use radiation interaction with tissue to produce diagnostic images. Mastering acoustic impedance and reflection here will also help you answer cross-topic wave questions in Paper 4.