Acoustic impedance (Z)
Medical Imaging - OCR A-Level Physics
Key Definition
Acoustic impedance (Z)
The product of the density of the medium and the speed of sound in that medium. Determines how much ultrasound is reflected at a boundary.
The product of the density of the medium and the speed of sound in that medium. Determines how much ultrasound is reflected at a boundary.
$$Z = \rho c$$
- When ultrasoundSound waves with frequencies above 20 kHz (beyond human hearing). Medical ultrasound typically uses 1-15 MHz. hits a boundary between two materials with different acoustic impedances Z_1 and Z_2, some is reflected and some is transmitted.
- The fraction of intensityThe powerThe rate of energy transfer. Measured in watts (W). transmitted per unit area perpendicular to the wave direction. Measured in W m⁻². Proportional to amplitude squared. reflected depends on the impedance mismatch.
- A large impedance mismatch means strong reflection (e.g. soft tissue to bone, or tissue to air).
- A small impedance mismatch means most ultrasoundSound waves with frequencies above 20 kHz (beyond human hearing). Medical ultrasound typically uses 1-15 MHz. is transmitted (e.g. between similar soft tissues).
$$\frac{I_r}{I_0} = \left(\frac{Z_2 - Z_1}{Z_2 + Z_1}\right)^2$$
Common Mistake
MEDIUM
Wrong: Forgetting to square the impedance fraction when calculating reflected intensityThe powerThe rate of energy transfer. Measured in watts (W). transmitted per unit area perpendicular to the wave direction. Measured in W m⁻². Proportional to amplitude squared..
Right: The reflection coefficient is the SQUARE of (Z₂ - Z₁)/(Z₂ + Z₁). Forgetting to square gives the amplitudeThe maximum displacement of a point on a wave from its equilibrium (rest) position. Measured in metres (m). ratio, not the intensityThe powerThe rate of energy transfer. Measured in watts (W). transmitted per unit area perpendicular to the wave direction. Measured in W m⁻². Proportional to amplitude squared. ratio.
Right: The reflection coefficient is the SQUARE of (Z₂ - Z₁)/(Z₂ + Z₁). Forgetting to square gives the amplitudeThe maximum displacement of a point on a wave from its equilibrium (rest) position. Measured in metres (m). ratio, not the intensityThe powerThe rate of energy transfer. Measured in watts (W). transmitted per unit area perpendicular to the wave direction. Measured in W m⁻². Proportional to amplitude squared. ratio.