Acoustic Impedance Calculator

Find the acoustic impedance (Z = density x speed of sound) of two media, then see how much sound intensity reflects and transmits at the boundary between them.

Quick Facts

Formula
Z = density x speed of sound (units: Rayl = kg/(m²·s))
Tissue and solids are usually reported in MRayl (10⁶ Rayl).
Reflection at a boundary
R = ((Z₂ − Z₁) / (Z₂ + Z₁))²
Bigger impedance mismatch means more reflected intensity.
Typical values
Soft tissue ≈1.6 MRayl, bone ≈7.8 MRayl, air ≈0.0004 MRayl
The huge tissue-air gap is why ultrasound gel is needed.

Your Results

Calculated
Z₁ (Medium 1 impedance)
-
density × speed of sound
Z₂ (Medium 2 impedance)
-
density × speed of sound
Reflection coefficient
-
Share of intensity reflected
Transmission coefficient
-
Share of intensity transmitted

Ready

Enter the density and speed of sound for both media, then press Calculate.

How to use the Acoustic Impedance Calculator

Acoustic impedance describes how strongly a medium resists the passage of a sound wave. It depends only on two properties of the medium: its density and the speed of sound through it. Once you know the acoustic impedance on each side of a boundary, you can predict what fraction of a sound wave's intensity bounces back (reflects) and what fraction continues through (transmits) — a relationship used throughout medical ultrasound, sonar, room acoustics, and audio engineering.

The formulas

  • Acoustic impedance: Z = ρ × c, where ρ (rho) is the medium's density in kg/m³ and c is the speed of sound in that medium in m/s. The result is in Rayls (kg/(m²·s)); dense materials are usually quoted in MRayl (1 MRayl = 1,000,000 Rayl).
  • Intensity reflection coefficient: for sound striking a boundary head-on (normal incidence), R = ((Z₂ − Z₁) / (Z₂ + Z₁))². This is the fraction of incident sound intensity that reflects back into medium 1.
  • Intensity transmission coefficient: T = 1 − R. This is the fraction that passes into medium 2. R and T always add up to 1 because energy is conserved at the boundary.

Reading the mismatch

  • When Z₁ and Z₂ are close, R is near 0 and almost all the sound transmits — this is called good "impedance matching."
  • When Z₁ and Z₂ are very different, R approaches 1 and most of the sound reflects instead of passing through.
  • The formula only depends on the ratio Z₂/Z₁, so swapping which medium the wave starts in does not change how much reflects.

Why this matters in practice

In medical ultrasound, the probe relies on reflections at tissue boundaries to build an image — a large impedance jump (like soft tissue to bone, or tissue to a gas pocket) produces a strong echo, which is why bone and gas show up so brightly and cast shadows on a scan. It is also why ultrasound gel is applied before scanning: skin next to air is such an extreme mismatch that virtually no sound would enter the body without it. The same physics governs sonar returns underwater and why soundproofing materials are chosen to mismatch impedance with air.

Frequently Asked Questions

What is acoustic impedance?
Acoustic impedance (Z) measures how much a medium resists the passage of a sound wave. It is defined as Z = ρ × c, where ρ is the medium's density and c is the speed of sound in that medium. The SI unit is the Rayl (kg/(m²·s)); values for tissue and other dense materials are usually given in MRayl (1 MRayl = 10⁶ Rayl).
How is the reflection coefficient calculated at a boundary?
For sound hitting a boundary straight on (normal incidence), the fraction of intensity reflected is R = ((Z₂ − Z₁) / (Z₂ + Z₁))², where Z₁ and Z₂ are the acoustic impedances of the two media. The remaining fraction, T = 1 − R, is transmitted into the second medium. A bigger impedance mismatch means more reflection.
Why is gel used in medical ultrasound?
Air has an acoustic impedance of roughly 0.0004 MRayl, while soft tissue is around 1.6 MRayl — a huge mismatch that would reflect almost all sound at a skin-air gap. Ultrasound gel has an impedance close to tissue, which removes the air gap and lets sound waves enter and exit the body instead of bouncing off the skin.
What units are used for acoustic impedance?
The SI unit is the Rayl, equal to 1 kg per square meter per second (kg/(m²·s)), named after Lord Rayleigh. Because biological tissues and solids have impedances in the millions of Rayls, results are typically reported in MRayl (megarayl) for readability.

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