Reflection at Boundaries

When ultrasound travels from a medium of acoustic impedance Z₁ into one of Z₂, part of it is reflected at the boundary. For a beam hitting the boundary at right angles, the fraction of the intensity reflected (the intensity reflection coefficient) isI_r / I₀ = (Z₂ − Z₁)² / (Z₂ + Z₁)²I_r is the reflected intensity and I₀ the incident intensity. The rest of the intensity is transmitted, so the fraction transmitted is 1 − I_r/I₀.• If Z₁ = Z₂, the fraction reflected is 0 and all the ultrasound passes on.
• The bigger the difference between Z₁ and Z₂, the larger the fraction reflected.Worked example 1: muscle (Z = 1.7 × 10⁶) to bone (Z = 7.8 × 10⁶ kg m⁻² s⁻¹).I_r/I₀ = (6.1 / 9.5)² = 0.41About 41% is reflected and 59% is transmitted, so bone gives a strong echo and little ultrasound reaches the tissue behind it.Worked example 2: air (Z = 430) to skin (Z = 1.7 × 10⁶ kg m⁻² s⁻¹).I_r/I₀ = (1.7 × 10⁶ − 430)² / (1.7 × 10⁶ + 430)² = 0.999Almost all the ultrasound is reflected, so hardly any would enter the body through a layer of air.