Calculate acoustic impedance and ultrasound reflection
Use Z = ρc to compare tissues and calculate the intensity reflected at a boundary.
Section 24 · Medical physics
A Level · Cambridge International Physics 9702, 2025–2027 syllabus. Topic 24 was checked against Cambridge’s 2028–2030 syllabus; the other remaining syllabus-year changes are still being reconciled. Online study supports the theory but cannot replace supervised practical work, full timed assessment or human subject-teacher review.
Before you begin
- Use exponential functions, wave speed, energy conservation and SI units; convert between joules and electronvolts when required.
Work on paper. Try each question before revealing help, and explain why your method works.
Quick readiness check
What two quantities define the specific acoustic impedance Z?
What you will learn
- Define specific acoustic impedance
- Calculate Z from density and sound speed
- Use the intensity reflection coefficient at a boundary
Impedance combines density and wave speed
The specific acoustic impedance of a medium is Z = ρc, where ρ is its density and c is the speed of sound in that medium. In SI units, Z is measured in kg m⁻² s⁻¹, also called a rayl.
A boundary between media with different Z values reflects some ultrasound. The greater the impedance mismatch, the larger the reflected fraction under the normal-incidence model.
The reflection coefficient is an intensity ratio
For a boundary between media with impedances Z₁ and Z₂, the intensity reflection coefficient is IR/I₀ = ((Z₁ − Z₂)/(Z₁ + Z₂))². It is a fraction, so multiply by 100 to express a percentage.
Keep the same impedance units on both sides. The ratio is dimensionless, and the squared difference means swapping the labels of the two media does not change the reflected fraction.
Pause and explain
What does IR/I₀ represent?
Worked example
Two media have acoustic impedances Z₁ = 1.50 MRayl and Z₂ = 1.65 MRayl. Calculate the intensity reflection coefficient.
Show the worked solution
- Use IR/I₀ = ((Z₁ − Z₂)/(Z₁ + Z₂))².
- The ratio is ((1.50 − 1.65)/(1.50 + 1.65))² = (−0.15/3.15)².
- The coefficient is 0.00227, which is 0.227%.
Answer IR/I₀ ≈ 2.27 × 10⁻³, or 0.227%.
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Test this topic →From guided practice to a new situation
Write your answer and reasoning first. Use a hint only if you are stuck. The model solution is for self-checking; your written work is not automatically marked.
A tissue has density 1000 kg m⁻³ and sound speed 1500 m s⁻¹. Calculate its acoustic impedance.
Give me a hint
Multiply density by speed and carry the SI units.
Compare my reasoning
- Z = ρc.
- Z = 1000 × 1500.
- Z = 1.50 × 10⁶ kg m⁻² s⁻¹ = 1.50 MRayl.
1.50 × 10⁶ kg m⁻² s⁻¹, or 1.50 MRayl.
Look for these in your work
- Uses Z = ρc
- Multiplies the given values
- States a compatible impedance unit
Calculate the reflected intensity fraction when Z₁ = 2.0 MRayl and Z₂ = 3.0 MRayl.
Give me a hint
Substitute into the squared impedance ratio.
Compare my reasoning
- IR/I₀ = ((2.0 − 3.0)/(2.0 + 3.0))².
- The ratio before squaring is −1.0/5.0 = −0.20.
- Squaring gives 0.040, or 4.0%.
0.040, or 4.0% of the incident intensity.
Look for these in your work
- Uses the difference over the sum
- Squares the ratio
- Converts the fraction to a percentage
A coupling gel is chosen so its acoustic impedance is close to the tissue’s. Explain how this can improve the ultrasound signal entering the tissue.
Give me a hint
Use the relationship between impedance mismatch and reflected intensity.
Compare my reasoning
- The reflection coefficient depends on the squared difference between the impedances relative to their sum.
- Making the gel and tissue impedances closer reduces that difference.
- A smaller reflected fraction means more incident intensity can pass into the tissue.
Closer impedances reduce reflection at the boundary, allowing more ultrasound intensity to enter the tissue.
Look for these in your work
- Links impedance mismatch to reflection
- Explains the effect of closer values
- Relates the smaller reflection to transmission into tissue
Common mistakes
- Forgetting to square the amplitude ratio
- Reporting the coefficient as a percentage without multiplying by 100
- Mixing impedance units between the two media
What can you explain now?
What two quantities define the specific acoustic impedance Z?
Compare with the explanation
Density and sound speed
The definition is Z = ρc.
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Make it stick
Why does the reflection coefficient contain a squared ratio?
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