Using ultrasound — OCR A-Level Physics

The piezoelectric effect is the production of a potential difference across certain crystals when they are mechanically deformed, and the reverse effect where an applied potential difference causes the crystal to change shape. An ultrasound transducer uses a piezoelectric crystal, such as quartz or lead zirconate titanate, to emit and receive ultrasound. In emission, an alternating potential difference is applied across the crystal, causing it to vibrate at the driving frequency and produce ultrasound. In reception, incoming ultrasound waves deform the crystal, generating a small alternating potential difference that can be detected and processed. In an MCQ, you may need to identify the correct sequence or distinguish emission from reception. Remember that the same transducer can perform both functions, often switching rapidly between them.

Ultrasound A-scan and B-scan are two display modes used in medical imaging. An A-scan (amplitude scan) displays the amplitude of reflected ultrasound pulses against time or depth on a single axis, producing a one-dimensional trace with peaks corresponding to boundaries between media. It is used, for example, in measuring the length of the eye or detecting flaws in materials. A B-scan (brightness scan) uses the same pulse-echo principle but displays the intensity of reflections as brightness on a two-dimensional image, building up a cross-sectional picture by scanning the transducer across the region. In an MCQ, you may be asked to match each scan type to its display or application. Remember that A-scan gives depth information along a line, while B-scan gives a 2D image.

Acoustic impedance Z of a medium is the product of its density ρ and the speed of ultrasound c in that medium, given by Z = ρc. The SI unit of Z is kg m⁻² s⁻¹, which is equivalent to Pa s m⁻¹. Acoustic impedance determines how much ultrasound is reflected at a boundary between two media: a large difference in Z produces a strong reflection, while a small difference produces weak reflection. For example, the acoustic impedance of soft tissue is about 1.6 × 10⁶ kg m⁻² s⁻¹, and that of air is much lower, so ultrasound is almost totally reflected at a tissue–air boundary. In an MCQ, you may be asked to calculate Z from ρ and c, or to compare reflection at different boundaries. Ensure you use consistent SI units: density in kg m⁻³ and speed in m s⁻¹.

When ultrasound meets a boundary between two media, part of the wave is reflected and part is transmitted. The reflected fraction depends on the acoustic impedances Z₁ and Z₂ of the two media. The intensity reflection coefficient is Iᵣ/I₀ = (Z₂ − Z₁)²/(Z₂ + Z₁)². Here I₀ is the incident intensity and Iᵣ is the reflected intensity. If Z₁ = Z₂, the numerator is zero, so no reflection occurs. A large impedance mismatch gives strong reflection. For example, at a soft-tissue–air boundary, Z₂ is much smaller than Z₁, so the fraction reflected is close to 1. This is why a coupling gel is needed in scanning. In an MCQ, you may be asked to calculate the ratio, identify the condition for maximum reflection, or explain why a gel improves transmission.

Acoustic impedance Z is a property of a medium that describes how much resistance it offers to the passage of ultrasound. It is defined as Z = ρc, where ρ is the density of the medium and c is the speed of ultrasound in that medium. The unit of Z is kg m⁻² s⁻¹. Values differ widely between media: air has a very low impedance, soft tissue is intermediate, and bone has a high impedance. This matters because the fraction of ultrasound reflected at a boundary depends on the difference in impedance between the two media. In an MCQ, you may be asked to calculate Z from density and speed, to identify its unit, or to compare impedances of different media.

Acoustic matching is the technique of choosing a coupling medium whose acoustic impedance is close to that of the skin, so that ultrasound passes efficiently from the transducer into the body. In ultrasound scanning, a special gel is applied between the transducer and the skin. The gel has an acoustic impedance similar to that of soft tissue, so it reduces the impedance mismatch at the skin surface. Without the gel, an air layer would cause almost total reflection because air has a very low impedance compared with skin. The gel also fills any irregularities between the transducer and the skin, ensuring good contact. In an MCQ, you may be asked why the gel is used, what property it must have, or what happens if it is omitted.

The Doppler effect occurs when ultrasound is reflected from moving blood cells. The frequency of the reflected wave is shifted by an amount Δf compared with the transmitted frequency f. The speed v of the blood can be found using Δf/f = (2v cos θ)/c, where c is the speed of ultrasound in blood and θ is the angle between the ultrasound beam and the direction of blood flow. The factor 2 arises because the ultrasound is Doppler shifted twice: once on the way to the moving cells and once on the way back. The cos θ term accounts for the component of blood velocity along the beam. In an MCQ, you may be asked to calculate v, to explain the factor 2, or to describe how θ affects the measurement.