Specific Acoustic Impedance (CIE A Level Physics)

• 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 Z_air = 400 kg m^-2 s^-1
• Skin has an acoustic impedance of Z_skin = 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

Refraction and reflection of ultrasound waves at a boundary between two materials with different acoustic impedances (in this case, Z₁ < Z₂ )

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