Acoustic Impedance Mismatch Calculator

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). These are the pairs behind the two material dropdowns, and every Z below is just the density times the speed.

Look at where the gel sits. It lands within 4% of soft tissue, which is the entire design brief for the stuff, while air is about four thousand times further away. Acrylic is in the list because it is what most ultrasound wear plates and NDT wedges are made from, and its impedance being roughly twice tissue rather than thousands of times off is why a probe works through one at all.

In sonar and NDE. The same equations apply to underwater sonar interfaces (water against sediment, water against a hull) and to non-destructive testing (NDT) of materials. A large impedance mismatch is useful in NDT rather than a problem, because it is what makes an internal crack or a delamination echo strongly. A crack is a steel-to-air interface, and steel to air reflects essentially everything.

Reading the answer in decibels. The calculator reports transmission loss as well as a percentage, because that is the unit on an ultrasound or NDT datasheet. It is 10·log₁₀(1/T_I) for one crossing, and a pulse-echo instrument pays it twice, once on the way out and once on the way back. Air against tissue is around 30 dB each way, which is why a millimetre of trapped air under the probe wipes out the image completely.