Acoustic impedance and ultrasound reflection

Overview

Recall questions on Acoustic impedance and ultrasound reflection.

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Questions from this subtopic

Each one with the model answer underneath.

1. 1

   Define the acoustic impedance of a medium and give the equation for it.

   Model answer

   The acoustic impedance is the product of the density of the medium and the speed of sound in it, Z = ρc, where ρ is the density in kg m⁻³ and c the speed of sound in m s⁻¹.

2. 2

   State the unit of acoustic impedance in SI base units.

   Model answer

   The unit is kg m⁻² s⁻¹.

3. 3

   Soft tissue has a density of 1060 kg m⁻³ and a speed of sound of 1540 m s⁻¹. Calculate its acoustic impedance.

   Model answer

   Z = ρc = 1060 × 1540 = 1.63 × 10⁶ kg m⁻² s⁻¹. Substituting back, 1.63 × 10⁶ ÷ 1540 returns a density of 1060 kg m⁻³.

4. 4

   Air has a density of 1.2 kg m⁻³ and a speed of sound of 340 m s⁻¹. Calculate its acoustic impedance.

   Model answer

   Z = ρc = 1.2 × 340 = 4.1 × 10² kg m⁻² s⁻¹. Substituting back, 408 ÷ 340 returns a density of 1.2 kg m⁻³.

5. 5

   State the equation for the fraction of ultrasound intensity reflected at a boundary between two media.

   Model answer

   The intensity reflection coefficient is the square of (Z₂ − Z₁)/(Z₂ + Z₁), where Z₁ and Z₂ are the acoustic impedances of the two media in kg m⁻² s⁻¹.

6. 6

   Calculate the fraction of ultrasound intensity reflected at a boundary between soft tissue of impedance 1.63 × 10⁶ kg m⁻² s⁻¹ and air of impedance 4.1 × 10² kg m⁻² s⁻¹.

   Model answer

   The difference of the impedances is 1.632 × 10⁶ and their sum is 1.633 × 10⁶, so the ratio is 0.9995 and its square is 0.999. Almost the whole beam, 99.9% of it, is reflected at such a boundary.

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