Acoustic Impedance Calculator — Z = ρc, Reflection & Transmission

Formula

How this is calculated

Acoustic impedance (Z) is a material property that describes how strongly a medium resists the propagation of sound. It is defined as Z = ρ × c, where ρ is the medium’s density in kg/m³ and c is the speed of sound in m/s. The unit is the rayl (1 rayl = 1 Pa·s/m = 1 kg/m²·s). Air has a very low impedance (~420 rayl), water a much higher one (~1.48 MRayl), and solid metals higher still (steel ~45 MRayl). Impedance mismatch between adjacent materials governs how sound behaves at an interface.

When a plane sound wave hits a boundary at normal incidence, the pressure reflection coefficient is r = (Z₂ − Z₁) / (Z₂ + Z₁). The intensity reflection coefficient (what detectors generally measure) is Rᵢ = r². The intensity transmission coefficient is Tᵢ = 1 − Rᵢ = 4Z₁Z₂ / (Z₁ + Z₂)². These two coefficients always sum to 1 (energy conservation), confirming that the interface neither creates nor destroys energy. If Z₁ = Z₂ (perfect match), Rᵢ = 0 and all energy is transmitted.

These equations assume perpendicular (normal) incidence of a plane wave; for oblique angles the calculation is more complex (Snell’s law plus boundary conditions). They also assume lossless, homogeneous, isotropic media with a perfectly flat, infinite interface. In practice, ultrasound coupling gels are used in medical imaging precisely to replace the air gap between the transducer and skin, reducing the massive air–tissue impedance mismatch and allowing enough energy to enter the body.