Acoustic impedance
Medical Imaging - OCR A-Level Physics
Worked Example
The acoustic impedanceThe product of the densityMass per unit volume of a material. Measured in kg m⁻³. of a medium and the speed of sound in that medium. Determines how much ultrasoundSound waves with frequencies above 20 kHz (beyond human hearing). Medical ultrasound typically uses 1-15 MHz. is reflected at a boundary. of soft tissue is 1.63 × 10⁶ kg m⁻² s⁻¹ and of bone is 7.78 × 10⁶ kg m⁻² s⁻¹. Calculate the fraction of ultrasoundSound waves with frequencies above 20 kHz (beyond human hearing). Medical ultrasound typically uses 1-15 MHz. 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 at a tissue-bone boundary.
Show Solution
1
Use the reflection equation
$I_r/I_{0} = ((Z_{2} - Z_{1})/(Z_{2} + Z_{1}))^{2}.$
2
$Z_{1} = 1.63 \times 10⁶, Z_{2} = 7.78 \times 10⁶.$
3
Z₂ - $Z_{1} = 6.15 \times 10⁶. Z_{2} + Z_{1} = 9.41 \times 10⁶$.
4
$Ratio = 6.15 \times 10⁶ / 9.41 \times 10⁶ = 0.653.$
5
Fraction reflected = (0.653)² = 0.427 ≈ 43%.
Answer
Approximately 43% of the ultrasoundSound waves with frequencies above 20 kHz (beyond human hearing). Medical ultrasound typically uses 1-15 MHz. 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. is reflected at the tissue-bone boundary. This large reflection is why ultrasound cannot image through bone effectively.