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AS & A-Level Physics 24 — Physics in Medical Imaging

AS & A-Level Physics 24 — Physics in Medical Imaging

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Independent Deckloop revision aligned with the Cambridge International AS & A Level Physics (9702) syllabus, 2025–2027. Not affiliated with or endorsed by Cambridge International Education. Chapter 24 of 26: Physics in medical imaging. Concepts, worked applications and misconception checks.

Physics EN A-Level
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Generating and Detecting Ultrasound with Piezoelectric Transducers

A piezoelectric transducer is a device that uses a piezoelectric crystal to generate and detect ultrasound waves. For generation, an alternating voltage is applied across the crystal. If the frequency of this alternating voltage matches the crystal's natural resonant frequency, the crystal vibrates with maximum amplitude due to resonance. These strong mechanical vibrations then produce high-frequency sound waves, i.e., ultrasound, in the surrounding medium. For detection, when ultrasound waves from the body strike the same crystal, the pressure variations cause it to deform. This mechanical deformation, through the direct piezoelectric effect, generates an alternating e.m.f. across the crystal, which can be amplified and processed. Thus, the same crystal serves as both an emitter and a receiver.

Key points

  • Ultrasound generation: An alternating voltage at the crystal's natural frequency causes resonant vibrations, producing ultrasound.
  • Ultrasound detection: Incident ultrasound waves deform the crystal, generating an alternating e.m.f.
  • The transducer acts as both a transmitter and a receiver.
  • Resonance is key for efficient ultrasound generation with significant amplitude.

Worked example

Question

An ultrasound transducer uses a piezoelectric crystal with a natural frequency of 5.0 MHz. Explain why applying a 5.0 MHz alternating voltage is more effective for generating ultrasound than a 1.0 MHz alternating voltage of the same amplitude.

Solution

1. The natural frequency of a piezoelectric crystal is the frequency at which it will vibrate with the largest amplitude when subjected to an external oscillating force or voltage.
2. Applying an alternating voltage at 5.0 MHz matches the crystal's natural resonant frequency. This causes the crystal to resonate, leading to significantly larger amplitude vibrations.
3. These larger amplitude vibrations efficiently transfer energy to the surrounding medium, generating powerful ultrasound waves.
4. Applying a 1.0 MHz voltage, which is far from the natural frequency, will result in much smaller amplitude vibrations, leading to very weak or negligible ultrasound generation, even with the same voltage amplitude.

Applying a 5.0 MHz alternating voltage causes the piezoelectric crystal to resonate, leading to maximum amplitude vibrations and efficient ultrasound generation. A 1.0 MHz voltage, being off-resonance, would produce much weaker vibrations and thus less effective ultrasound.

Common pitfalls

  • Forgetting the role of resonance in maximising the amplitude of vibrations for efficient ultrasound generation.
  • Not understanding that the same crystal can perform both generation and detection functions.

Prerequisites

  • Understanding of the fundamental piezoelectric effect.
  • Knowledge of wave generation and frequency.
  • Understanding of longitudinal waves (sound).
Further resources