Using ultrasound: (f) impedance

The idea

Acoustic impedance Z is a property of a medium that describes how much resistance it offers to the passage of ultrasound. It is defined as Z = ρc, where ρ is the density of the medium and c is the speed of ultrasound in that medium. The unit of Z is kg m⁻² s⁻¹. Values differ widely between media: air has a very low impedance, soft tissue is intermediate, and bone has a high impedance. This matters because the fraction of ultrasound reflected at a boundary depends on the difference in impedance between the two media.

What earns the marks

• Define acoustic impedance as Z = ρc, where ρ is density and c is the speed of ultrasound in the medium.
• State the unit of acoustic impedance as kg m⁻² s⁻¹.
• Calculate acoustic impedance from given values of density and speed.
• Compare acoustic impedances of different media, such as air, soft tissue and bone.
• Relate impedance mismatch to the intensity reflection coefficient.

Common mistakes and how to put them right

• Confusing acoustic impedance with electrical impedance.

  Put it right: They are different quantities with different units.

• Using the wrong unit, such as kg m⁻² s⁻² or kg m⁻³ s⁻¹.

  Put it right: The correct unit is kg m⁻² s⁻¹.

• Forgetting that c is the speed of ultrasound in the medium, not the speed of sound in air.

• Mixing up density and speed when substituting into Z = ρc.

Exam tips

• Check that density is in kg m⁻³ and speed is in m s⁻¹ before multiplying.
• Use the unit to check your calculation: kg m⁻³ × m s⁻¹ = kg m⁻² s⁻¹.
• Remember that impedance is a property of the medium, not of the wave.
• In multiple-choice questions, eliminate options with incorrect units or unrealistic magnitudes.