Hong Life CalculatorsUnderstanding the acoustic impedance calculator — concept and principle
Acoustic impedance describes how strongly a material resists the passage of sound. This calculator finds the impedance of two media and, for a sound wave hitting the boundary head-on, how much is reflected and how much passes through. It is used in ultrasound imaging, non-destructive testing, sonar and acoustics.
How it is calculated
- Characteristic impedance Z = ρc (density × speed of sound), in kg/(m²·s) = rayl; 1 MRayl = 10⁶ rayl.
- Pressure reflection coefficient r = (Z₂ − Z₁) ÷ (Z₂ + Z₁).
- Pressure transmission coefficient t = 2Z₂ ÷ (Z₁ + Z₂).
- Reflected intensity R = r²; transmitted intensity T = 1 − R.
- Transmission loss (dB) = −10 log₁₀ T.
The principle
At a boundary, the pressure and particle velocity must be continuous on both sides. Solving those two conditions for an incoming, reflected and transmitted wave gives the coefficients above. When impedances match, nothing is reflected. When they differ greatly, most energy bounces back. The pressure transmission coefficient can exceed 1 going into a much stiffer medium, but the transmitted intensity is still small because intensity also depends on impedance.
Worked example
Default inputs: medium 1 water (1,000 kg/m³, 1,500 m/s); medium 2 steel (7,800 kg/m³, 5,960 m/s).
- Z₁ = 1,000 × 1,500 = 1,500,000 kg/(m²·s) = 1.5 MRayl.
- Z₂ = 7,800 × 5,960 = 46.488 MRayl.
- r = (46.488 − 1.5) ÷ (46.488 + 1.5) ≈ 0.9375; t = 2 × 46.488 ÷ 47.988 ≈ 1.9375.
- Intensity reflected = 0.9375² ≈ 87.89%; transmitted ≈ 12.11%.
- Transmission loss = −10 log₁₀ 0.1211 ≈ 9.17 dB.
| Density of medium 1 (kg/m³) | Acoustic impedance Z₁ (MRayl) |
|---|---|
| 250 | 0.375 |
| 500 | 0.75 |
| 750 | 1.125 |
| 1,000 | 1.5 |
| 1,250 | 1.875 |
| 1,500 | 2.25 |
| 2,000 | 3 |
How to read the result
A large mismatch, such as between air and skin, reflects almost all sound, which is why ultrasound gel is used between the probe and the body. Matching layers in transducers are designed with intermediate impedances to improve transmission. A negative r means the reflected pressure wave is inverted.
Common mistakes
- Mixing longitudinal and shear wave speeds in solids.
- Confusing pressure and intensity coefficients.
- Applying normal-incidence formulas to oblique waves.
- Forgetting that absorption inside the materials is not included.
Frequently asked questions
What is the acoustic impedance of water?
About 1.5 MRayl, from a density of about 1,000 kg/m³ and a sound speed of about 1,500 m/s.
Why is ultrasound gel needed?
Air has a very low impedance, so an air gap would reflect almost all the ultrasound.
Can the transmission coefficient be greater than 1?
For pressure, yes; for intensity, no. Energy is conserved, so R + T = 1.
Sources: Kinsler, Frey, Coppens & Sanders, Fundamentals of Acoustics, 4th ed. Wiley · Kuttruff, H., Acoustics: An Introduction. Taylor & Francis