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Acoustic impedance: what it means and why it matters

Angle Beam editorial teamUpdated 4 min read

Acoustic impedance, written Z, is a material's density multiplied by the speed of sound in it. When a sound wave meets a boundary between two materials, the difference in their impedances decides how much energy is reflected and how much passes through. A large difference means strong reflection and little transmission.

Two interfaces: a large impedance difference reflects most of the energy, a small difference transmits most of it
Arrow thickness shows the share of intensity. Reflected is R and transmitted is 1 minus R.
Use this diagram

The formulas

Impedance is Z = ρ × c, density times the wave velocity for the mode in use. For normal incidence, the fraction of intensity reflected is R = ((Z2 − Z1) / (Z2 + Z1))², and the fraction transmitted is 1 − R. The pressure reflection coefficient has no square: (Z2 − Z1) / (Z2 + Z1). It changes sign when the wave goes from a high impedance to a low one, meaning the reflected pulse is inverted. Check whether a question asks about intensity or about pressure.

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A worked example

Steel is about 7.85 g/cm³ with a longitudinal velocity near 5.9 km/s, so Z is about 46. Water is about 1.0 g/cm³ at 1.48 km/s, so Z is about 1.48. With those values, R = ((1.48 − 46) / (1.48 + 46))² = (−44.52 / 47.48)² = 0.88. About 88 percent of the intensity reflects off a steel surface in water and about 12 percent enters the steel. The same sums for steel and air give a reflection above 99.99 percent, which is the reason a probe needs couplant.

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Where it matters in a test

  • Entering the part. Couplant, wedge and part all have different impedances, so some energy is lost at each boundary.
  • Reflecting off flaws. A flaw filled with air or gas is a very strong reflector. A flaw filled with something closer in impedance to the part, such as a slag-like inclusion, can reflect less.
  • Bond testing. The echo from a good bond and a disbond differ because the impedance on the far side of the interface is different.

Mix-ups to avoid

  • Impedance versus velocity. Velocity is one factor in impedance. Two materials with the same velocity can have different impedance if their densities differ.
  • Impedance versus attenuation. Impedance sets what happens at a boundary. Attenuation sets what happens along the path.
  • Intensity versus pressure. The squared formula is for intensity. Reading a question's wording prevents a wrong answer from the right method.
  • Which mode. Use the velocity of the wave mode you are working with. A shear wave in the same steel has a different impedance than a longitudinal wave.

How the exam uses it

Expect questions on the definition, on which interface gives the strongest reflection (the largest impedance difference), on why couplant is needed, and on direct calculations with a table of densities and velocities. Keep the units straight: g/cm³ times km/s gives 10⁶ kg/(m²·s) directly.

Topic names here follow the UT General outline for exams before 5 February 2027; the UT outline change guide shows how the later list lines up.

Practice it

Work your own pairs of materials in the acoustic impedance calculator, run a few more of these sums in the NDT math drill, and compare with the worked method in the UT formulas guide. The most common practical consequence is explained in couplant, and the choice of wave mode that sets the velocity in Z is in shear vs longitudinal waves. The full list is in the NDT terms glossary.

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Sources

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Background reading: Evident's published UT material and ASNT's published topic headings. Outline checked 25 October 2026.

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