CIE A Level Physics (9702) 2019-2021

Revision Notes

19.3.2 Specific Acoustic Impedance

Specific Acoustic Impedance

  • The acoustic impedance, Z, of a medium is defined as:

The product of the speed of the ultrasound in the medium and the density of the medium

  • This quantity describes how much resistance an ultrasound beam encounters as it passes through a tissue
  • Acoustic impedance can be calculated using the equation:

Z = ρc

  • Where:
    • Z = acoustic impedance (kg m-2 s-1)
    • ρ = the density of the material (kg m-3)
    • c = the speed of sound in the material (m s-1)
  • This equation tells us:
    • The higher the density of a tissue, the greater the acoustic impedance
    • The faster the ultrasound travels through the material, the greater the acoustic impedance also
  • This is because sound travels faster in denser materials
    • Sound is fastest in solids and slowest in gases
    • The closer the particles in the material, the faster the vibrations can move through the material
  • At the boundary between media of different acoustic impedances, some of the wave energy is reflected and some is transmitted
  • The greater the difference in acoustic impedance between the two media, the greater the reflection and the smaller the transmission
    • Two materials with the same acoustic impedance would give no reflection
    • Two materials with a large difference in values would give much larger reflections
  • Air has an acoustic impedance of Zair = 400 kg m-2 s-1
  • Skin has an acoustic impedance of Zskin = 1.7 × 106 kg m-2 s-1
    • The large difference means ultrasound would be significantly reflected, hence a coupling gel is necessary
    • The coupling gel used has a similar Z value to skin, meaning that very little ultrasound is reflected

Worked example: Calculating bone density

Specific_Acoustic_Impedance_Worked_Example_-_Calculating_Density_of_Bone_Question, downloadable AS & A Level Physics revision notes

Step 1:            Write down known quantities

Acoustic impedance of bone, Z = 7.0 × 106 kg m-2 s-1

Speed of ultrasound in bone, c = 4100 m s-1

Step 2:            Write out the equation for acoustic impedance

Z = ρc

Step 3:            Rearrange for density and calculate

Specific Acoustic Impedance Worked Example equation

Exam Tip

A common mistake is to confuse the c in the acoustic impedance equation for the speed of light – don’t do this!

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