Cambridge A Levels A2 Physics Chapter 24 Medical Physics
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Cambridge A Levels A2 Physics
Institution
Chapter 24 Medical Physics: 46 pages
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Chapter 24 Medical Physics
24.1 Production and Use of Ultrasound
Ultrasound
Ultrasound is sound with frequencies above the range of human hearing, typically above about 20kHz.
Generating Ultrasound
In ultrasound scanning, ultrasonic waves are produced by a varying electrical voltage in a transducer.
The same device also acts as a detector.
Ultrasound waves can be generated using a piezo-electric transducer.
A transducer is a device that converts energy from one form to another.
In this case, electrical energy is converted into ultrasound energy by means of a piezo-electric crystal such as
quartz.
The Piezo-electric Transducer
Piezo-electric effect
The ability of materials to generate a potential difference by transferring mechanical energy
to electrical energy.
An applied voltage causes a piezo-electric crystal to contract or expand.
When a voltage is applied across it in one direction, it shrinks slightly.
When the voltage is reversed, it expands slightly.
So, an alternating voltage with frequency f causes the crystal to contract and expand at the same frequency f.
The voltage induces a strain in the crystal.
An applied stress causes an induced e.m.f. across the crystal.
,Piezo-electric Crystal
At the heart of a piezoelectric transducer is a piezoelectric crystal.
Piezoelectric crystals are materials which produce a potential difference when they are deformed.
This deformation can be by compression or stretching.
The structure of quartz is made up of a large number of tetrahedral silicate units which build up to form a
crystal of quartz.
When the crystal is unstressed, the centres of charge of the positive and the negative ions in any one unit
coincide (Figure 24.3a).
If a potential difference is applied to a piezoelectric crystal, then it deforms, and if the potential difference is
reversed, then it expands.
i. Electrodes may be formed on opposite sides of the crystal by depositing silver on its surfaces.
ii. When a potential difference is applied between the electrodes, an electric field is set up in the crystal.
iii. This field causes forces to act on the ions.
iv. The oxygen ions are negatively charged and the silicon ions have a positive charge.
v. The ions are not held rigidly in position and, as a result, they will be displaced slightly when the electric
field is applied across the crystal.
vi. The positive ions will be attracted towards the negative electrode and the negative ions will be
attracted to the positive electrode.
vii. Dependent on the direction of the electric field, the crystal will become slightly thinner (Figure 24.3b) or
slightly thicker (Figure 24.3c).
,viii. When the lattice is distorted, the structure becomes charged creating an electric field and, as a result,
an electric current.
ix. If an electric current is applied to the crystal, then this causes the shape of the lattice to alternate
which produces a sound wave.
x. Due to the conventional direction of electric current, it will flow from the positive to the negative
region of the crystal.
, Generating Ultrasound
In a piezo-electric transducer, an alternating voltage is applied across the crystal, which then acts as the
vibrating source of ultrasound waves.
▪ An alternating voltage applied across the electrodes causes the crystal to vibrate with a frequency
equal to that of the applied voltage.
▪ These oscillations are likely to have a small amplitude.
However, if the frequency of the applied voltage is equal to the natural frequency of vibration of the
crystal, resonance will occur and the amplitude of vibration will be maximum.
▪ The dimensions of the crystal can be such that the oscillations are in the ultrasound range of
frequencies (greater than about 20kHz).
These oscillations will give rise to ultrasound waves in any medium surrounding the crystal.
Detecting Ultrasound
The transducer also acts as the detector of reflected ultrasound waves.
It can do this because the piezo-electric effect works in reverse:
a varying stress applied to the crystal produces a varying e.m.f. across the crystal.
To maximise the effect, the frequency of the waves must match the resonant frequency of the crystal.
The optimum size of the crystal is half the wavelength of the ultrasound waves.
𝝀
𝑶𝒑𝒕𝒊𝒎𝒖𝒎 𝒔𝒊𝒛𝒆 𝒐𝒇 𝒄𝒓𝒚𝒔𝒕𝒂𝒍 =
𝟐
If a stress is applied to an uncharged quartz crystal, the forces involved will alter the positions of the positive
and the negative ions, creating a potential difference across the crystal.
Therefore, if an ultrasound wave is incident on the crystal, the pressure variations in the wave will give rise to
voltage variations across the crystal. An ultrasound transducer may, therefore, also be used as a detector (or
receiver).
Summary:
A piezoelectric crystal can act as both a receiver or transmitter of ultrasound,
▪ When it is receiving ultrasound, it converts the sound waves into an alternating p.d.
▪ When it is transmitting ultrasound, it converts an alternating p.d. into sound waves.
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