Acoustic Impedance (OCR A Level Physics): Revision Note

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 shows:

  • 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

• Sound is fastest in solids and slowest in gases

  • Sound is usually fastest in solids because they are much stiffer

• 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 )

Impedance Matching in Ultrasound Scans

• The intensity reflection coefficient α is defined as:

The ratio of the intensity of the reflected wave relative to the incident (transmitted) wave

• This can be calculated using the fraction:

$\alpha =\frac{I_r}{I_0}=\frac{(Z_2-Z_1{)}^2}{(Z_2+Z_1{)}^2}$

• Where:

  • α = intensity reflection coefficient

  • I_R = intensity of the reflected wave (W m^-2)

  • I₀ = intensity of the incident wave (W m^-2)

  • Z₁ = acoustic impedance of one material (kg m^-2 s^-1)

  • Z₂ = acoustic impedance of a second material (kg m^-2 s^-1)

• This ratio shows:

  • If there is a large difference between the impedance of the two materials, then most of the energy will be reflected

  • If the impedance is the same, then there will be no reflection

Coupling Medium

• When ultrasound is used in medical imaging, a coupler is needed between the transducer and the body

  • This is because the acoustic impedance of the soft tissues of the body is much greater than that of air

• If air is present between the transducer and the body, then almost all the ultrasound energy will be reflected

• To counter this, a coupling gel is placed between the transducer and the body

  • This is because skin and coupling gel have a similar acoustic impedance, so little ultrasound is reflected

• This is an example of impedance matching, which is defined as when:

Two media have a similar acoustic impedance, resulting in little to no reflection of the ultrasound wave

• In terms of intensity reflection coefficient, α, between the two media:

  • At lower values of α, the media are impedance matched, so less reflection occurs

  • At higher values of α, the media are not impedance matched, so more reflection occurs