Acoustic Impedance Mismatch Calculator
Calculate acoustic impedance for two materials and find reflection and transmission coefficients at the interface.
Used in ultrasound, sonar, and acoustic design.
Acoustic impedance Z is the product of a material’s density and the speed of sound in that medium:
Z = rho * c (units: kg/m^2/s, or Rayl)
When a sound wave crosses an interface between two materials with different impedances, part of the wave reflects and part transmits. The amplitude reflection coefficient is:
R = (Z2 - Z1) / (Z2 + Z1)
A positive R means the reflected wave is in phase with the incident wave (Z2 > Z1). A negative R means phase inversion. The intensity reflection coefficient (energy reflected) is R^2, and intensity transmission is:
T_I = 1 - R^2 = 4 * Z1 * Z2 / (Z1 + Z2)^2
Why impedance matching matters. Perfect transmission requires Z1 = Z2. In medical ultrasound, a gel is applied between the transducer and skin precisely because air (Z = 413 Rayl) and tissue (Z ~ 1.6 million Rayl) are so mismatched that almost all ultrasound would reflect off an air gap. The gel has impedance close to tissue, allowing most energy to transmit.
Reference values (approximate). Air: rho = 1.2 kg/m^3, c = 343 m/s, Z = 413 Rayl. Water: 1000 kg/m^3, 1480 m/s, Z = 1.48 MRayl. Soft tissue: ~1060 kg/m^3, ~1540 m/s, Z = 1.63 MRayl. Bone: ~2000 kg/m^3, ~4000 m/s, Z = 8 MRayl. Steel: ~7800 kg/m^3, ~5900 m/s, Z = 46 MRayl.
In sonar and NDE. The same equations apply to underwater sonar interfaces (water/sediment, water/hull) and non-destructive evaluation (NDT) of materials. A large impedance mismatch is actually useful in NDT — it means strong echoes from internal cracks or delaminations.