Ultrasound imaging (A-level only) — AQA A-Level Physics

Ultrasound imaging is a medical diagnostic technique that uses high-frequency sound waves, typically in the range 1-20 MHz, to visualise internal body structures. In AQA A-Level Physics, you study the physics principles behind ultrasound: the piezoelectric effect used to generate and detect pulses, the reflection and transmission of ultrasound at tissue boundaries, and the use of the Doppler effect to measure blood flow velocity. This topic sits within the 'Medical Physics' option and builds on your understanding of waves, including reflection, refraction, and the Doppler effect.

Understanding ultrasound imaging is important because it is a safe, non-ionising alternative to X-rays and CT scans, widely used in obstetrics and cardiology. The physics you learn here explains why a coupling gel is needed, why bone casts a strong echo, and how doctors can detect blockages in arteries. It also reinforces core wave concepts and provides a real-world context for calculations involving acoustic impedance and intensity reflection coefficients.

• →Ultrasound is sound with frequency above 20 kHz, beyond the range of human hearing. Medical ultrasound typically uses frequencies of 1-20 MHz to achieve good resolution with acceptable penetration depth.
• →The piezoelectric effect: certain crystals (e.g., quartz, lead zirconate titanate) deform when a voltage is applied across them (generating ultrasound) and produce a voltage when deformed by incident ultrasound (detecting echoes).
• →Acoustic impedance Z = ρc, where ρ is the density of the medium and c is the speed of sound in it. The intensity reflection coefficient at a boundary is α = (Z2 - Z1)^2 / (Z2 + Z1)^2.
• →A coupling gel is used between the transducer and skin to eliminate the air gap, because the acoustic impedance of air is very different from that of skin, which would cause almost total reflection at the skin surface.
• →The Doppler effect is used to measure blood flow: Δf = (2 f0 v cos θ)/c, where v is the speed of blood, θ is the angle between the beam and the flow direction, and c is the speed of sound in tissue.

• Acoustic impedance is defined as Z = ρc, the product of tissue density and speed of sound in that tissue.
• At a boundary, the reflected and transmitted intensities depend on the difference in acoustic impedance between the two media.
• The intensity reflection coefficient is (Z₂ − Z₁)²/(Z₂ + Z₁)², giving the fraction of incident intensity reflected.
• A large impedance mismatch, such as tissue to air, reflects most of the ultrasound, while a small mismatch transmits most of it.
• Attenuation is the reduction in intensity with distance due to absorption, scattering and reflection, and it increases with ultrasound frequency.
• Coupling gel is used because it has an impedance close to that of skin, reducing reflection at the skin–air boundary.
• Pulses are used so that the time delay of each echo can be measured and related to the depth of a boundary.
• Ultrasound is non-ionising, so it avoids the radiation risk associated with X-rays and CT scans, making it safer for fetuses and repeated examinations.
• Real-time imaging allows movement such as heart valves or blood flow to be observed, which static X-ray images cannot show directly.
• Resolution is limited by wavelength; using a higher frequency shortens wavelength and improves resolution but increases attenuation in tissue, reducing penetration depth.
• Strong reflection occurs at boundaries with large acoustic impedance mismatch, such as soft tissue to bone or air, which can obscure structures behind them.
• Ultrasound equipment is relatively cheap, portable and widely available compared with MRI, though image quality depends heavily on operator skill.
• Safety concerns include tissue heating and cavitation from high-intensity ultrasound; diagnostic exposure is controlled by limiting intensity and scan time.
• A piezoelectric material converts an applied alternating voltage into mechanical vibration, generating an ultrasound pulse at the driving frequency.
• The same piezoelectric crystal detects returning echoes because incident sound deforms it and generates a small alternating voltage.
• The transducer is driven at its resonant frequency to produce maximum amplitude output, and damping shortens the pulse to improve resolution.
• Coupling gel excludes air between transducer and skin because the large acoustic impedance mismatch at an air boundary would reflect nearly all the ultrasound.
• The time delay between pulse emission and echo detection gives reflector depth using d = vt/2, where v is the speed of sound in the medium.
• Echo amplitude depends on the acoustic impedance difference at a boundary, so larger mismatches produce stronger echoes.
• Describes an A-scan as a one-dimensional amplitude–time graph in which echo spikes are plotted against time.
• Explains that in an A-scan the vertical spike height represents echo amplitude and the horizontal position represents time, allowing depth to be calculated using distance = speed × time ÷ 2.
• Describes a B-scan as a two-dimensional image formed by moving the transducer and combining many A-scan lines.
• Explains that in a B-scan the brightness of each point represents echo amplitude, so boundaries between tissues of different acoustic impedance appear as bright lines.
• Applies the pulse–echo principle to both scans, including the need for a coupling medium and the use of the speed of sound in tissue.
• Compares the information provided: A-scans give precise depth measurements along one line, while B-scans give spatial structure across a plane.
• States at least two valid medical applications of ultrasound imaging, such as prenatal scanning, echocardiography, or eye measurement.
• Explains that ultrasound is used because it is non-ionising and therefore safer than X-rays for repeated or prenatal imaging.
• Links applications to the pulse–echo principle: a pulse is reflected at a boundary where acoustic impedance changes, and the echo time gives depth.
• Describes how a coupling medium such as gel is used to reduce reflection at the transducer–skin boundary and transmit ultrasound into the body.
• Explains how the amplitude of the returning echo depends on the difference in acoustic impedance between two media.
• Applies the depth equation distance = speed × time ÷ 2 to a stated medical application, for example measuring the distance to a foetal skull.

• 💡Write the equation Z = ρc and the reflection coefficient before substituting values, and keep units consistent.
• 💡Check that a calculated reflection coefficient is between 0 and 1, and interpret it as a fraction or percentage.
• 💡Explain coupling gel in terms of impedance matching rather than simply saying it helps sound travel.
• 💡When discussing attenuation, state that higher frequency gives better resolution but greater attenuation.
• 💡Compare ultrasound with a named alternative such as X-ray, CT or MRI, and make each advantage or disadvantage explicit rather than listing features of ultrasound alone.
• 💡Link resolution to wavelength and frequency using v = fλ, and link penetration to attenuation, so the trade-off is clear.
• 💡Use precise safety vocabulary such as ionising radiation, heating and cavitation, and avoid vague phrases like safer rays.
• 💡Describe the sequence emission, propagation, reflection, detection and timing, so the role of the piezoelectric crystal is clear at each stage.
• 💡When calculating depth, identify the total travel time and divide by two before multiplying by speed, or use d = vt/2 directly.
• 💡Use the term acoustic impedance mismatch when explaining echo strength, and link it to reflection at tissue boundaries.
• 💡When describing an A-scan, always state what the vertical and horizontal axes represent before interpreting a trace.
• 💡When calculating depth from an echo time, write the full equation distance = speed × time ÷ 2 and substitute values with units.
• 💡When comparing A-scans and B-scans, use the terms one-dimensional and two-dimensional explicitly and link each to its display method.
• 💡When asked for applications, give named medical examples and state the physical principle each relies on, rather than listing names alone.
• 💡Use the phrase non-ionising when explaining the safety advantage of ultrasound over X-rays.
• 💡Always define your symbols clearly when using formulas. For example, state that Z is acoustic impedance, ρ is density, and c is the speed of sound. This helps you avoid confusion and shows the examiner you understand the physics.
• 💡When calculating the intensity reflection coefficient, remember to square the difference and the sum. A common error is to forget to square the terms, leading to an incorrect answer.
• 💡In Doppler questions, pay attention to the angle θ. If the question states the beam is parallel to the blood flow, then θ = 0° and cos θ = 1. If an angle is given, you must use cos θ. Also, remember the factor of 2 in the formula.

• Confusing acoustic impedance with resistance or with intensity; correct this by defining Z as density multiplied by speed of sound.
• Using the impedance values the wrong way round in the reflection coefficient; correct this by squaring the difference and the sum so the result is unchanged by swapping Z₁ and Z₂.
• Believing all ultrasound is reflected at every boundary; correct this by explaining that the reflected fraction depends on the impedance mismatch.
• Ignoring attenuation when comparing echoes from different depths; correct this by noting that deeper echoes are weaker because intensity falls with distance.
• Claiming ultrasound is completely risk-free: correct this by stating that diagnostic levels are kept low to minimise heating and cavitation, so risk is reduced rather than absent.
• Confusing resolution with penetration: correct this by explaining that higher frequency improves resolution but is attenuated more, so penetration decreases.
• Stating that ultrasound cannot image bone at all: correct this by saying bone reflects strongly, producing bright surfaces, but little sound passes through to image deeper structures.
• Thinking a separate transmitter and receiver are always needed: correct this by explaining that one piezoelectric crystal can both generate and detect ultrasound.
• Ignoring the factor of one half in depth calculations: correct this by using d = vt/2 because the pulse travels to the boundary and back.
• Assuming coupling gel improves the piezoelectric effect: correct this by stating that gel provides acoustic coupling and reduces reflection at the air–skin boundary.
• Confusing the axes of an A-scan: the error is treating the horizontal axis as depth directly; the correction is that the horizontal axis is time, and depth is calculated from time using distance = speed × time ÷ 2.
• Stating that a B-scan uses spike height to show echo amplitude: the error is carrying over the A-scan display convention; the correction is that a B-scan uses brightness to represent echo amplitude.
• Forgetting the factor of two in depth calculations: the error is using distance = speed × time; the correction is that the pulse travels to the boundary and back, so distance = speed × time ÷ 2.
• Including industrial applications like testing welds: correct this by focusing exclusively on medical applications such as echocardiography for this option.
• Claiming ultrasound is ionising radiation: correct this by stating ultrasound consists of longitudinal pressure waves and is non-ionising.
• Using the one-way distance equation: correct this by calculating depth as speed × time ÷ 2, since the pulse travels to the boundary and back.
• Students often think that ultrasound imaging uses electromagnetic waves. Correction: Ultrasound is a mechanical (pressure) wave, not an electromagnetic wave. It requires a medium to travel through and cannot propagate through a vacuum.
• Many students believe that a higher frequency always gives a better image. Correction: Higher frequency gives better resolution (shorter wavelength) but is attenuated more rapidly in tissue, so there is a trade-off between resolution and penetration depth.
• Students sometimes assume that the intensity reflection coefficient depends only on the difference in acoustic impedance, ignoring the sum. Correction: The formula α = (Z2 - Z1)^2 / (Z2 + Z1)^2 shows that both the difference and the sum matter; a large difference relative to the sum gives a strong reflection.

1. 1Start by reviewing the basic properties of waves, especially reflection and the Doppler effect, to ensure a solid foundation.
2. 2Learn the definitions and formulas for acoustic impedance and intensity reflection coefficient. Practice calculations with different tissue types.
3. 3Understand the piezoelectric effect and how a transducer both emits and detects ultrasound pulses. Draw a diagram of the transducer and label the parts.
4. 4Study the Doppler ultrasound technique, including the formula and the significance of the angle θ. Work through example calculations.
5. 5Attempt past paper questions on ultrasound imaging, focusing on 6-mark structured questions that require explanations as well as calculations. Review mark schemes to understand what examiners expect.

• 📋Calculation of acoustic impedance or intensity reflection coefficient: You may be asked to calculate Z for a given tissue or the percentage of intensity reflected at a boundary. Always show your working and give units.
• 📋Explanation of the piezoelectric effect and transducer operation: Typically a 4-6 mark question asking you to describe how a transducer generates and detects ultrasound, including the role of the coupling gel.
• 📋Doppler shift calculation: You may be given a scenario with blood flow and asked to calculate the frequency shift or the speed of blood. Pay attention to the angle and the factor of 2.
• 📋Comparison of ultrasound with other imaging techniques: A structured question might ask you to compare ultrasound with X-rays or CT scans in terms of safety, resolution, and applications.