The Acoustic Impedance Calculator computes Z = ρ × c for any material and calculates reflection and transmission coefficients at boundaries between two media. Essential for ultrasound transducer design, architectural acoustics, sonar engineering, and non-destructive testing.
413
rayl
1,477,040
rayl
0.9994
1.9994
-4.9e-3
dB
413
rayl
1,477,040
rayl
0.9994
1.9994
-4.9e-3
dB
The calculator for acoustic impedance computes the specific acoustic impedance of any material from its density and speed of sound, then determines how sound waves behave at the boundary between two media — including the reflection coefficient (R), transmission coefficient (T), and the fraction of acoustic intensity that crosses the interface. Acoustic impedance is the fundamental property governing ultrasound imaging, sonar performance, noise barrier design, and non-destructive testing.
Specific acoustic impedance (Z) characterizes a medium's resistance to acoustic pressure waves:
Z = ρ × c (rayl = kg/m²·s)
where ρ is the medium's density (kg/m³) and c is the speed of sound in that medium (m/s). Water has Z ≈ 1.48 MRayl; soft tissue approximately 1.63 MRayl; air only 415 Rayl; steel approximately 47 MRayl. The enormous impedance mismatch between air (415 Rayl) and water (1,480,000 Rayl) means that less than 0.1% of acoustic energy crosses an air-water boundary without a coupling medium — which is why medical ultrasound requires gel between the transducer and skin. The speed of sound calculator provides the c values needed as inputs.
At a planar boundary between medium 1 (Z₁) and medium 2 (Z₂), the pressure reflection and transmission coefficients for normal incidence are:
Note that R + T ≠ 1 in general because these are pressure coefficients. The intensity reflection coefficient = R², and intensity transmission = 1 − R². When Z₁ = Z₂ (impedance-matched media), R = 0 and all energy transmits. When Z₁ ≫ Z₂ or Z₂ ≫ Z₁, R approaches ±1 and nearly all energy reflects. Use this online calculator to model boundary behavior for any material combination.
Acoustic impedance matching is the central engineering challenge in ultrasound transducer design. Medical ultrasound transducers use matching layers — materials with intermediate Z values — to maximize energy transfer from the piezoelectric crystal (Z ≈ 30 MRayl) into tissue (Z ≈ 1.6 MRayl). Without matching layers, the impedance mismatch would reflect over 85% of acoustic energy. In non-destructive testing (NDT), reflections from internal defects are detected because cracks and voids have Z ≈ 0 (air-filled), creating near-total reflection at the defect boundary. The sound intensity calculator, decibel calculator, and acoustics calculators category provide complementary tools for complete acoustic system analysis.
The specific acoustic impedance of a medium is the product of its density and the speed of sound within it:
$$Z = \rho \cdot c$$
where $$\rho$$ is the density in kg/m³ and $$c$$ is the speed of sound in m/s. The unit is the rayl (Pa·s/m).
When a sound wave encounters a boundary between two media with impedances $$Z_1$$ and $$Z_2$$, part of the wave is reflected and part is transmitted. For normal incidence, the pressure reflection coefficient is:
$$R = \frac{Z_2 - Z_1}{Z_2 + Z_1}$$
The pressure transmission coefficient is:
$$T = \frac{2Z_2}{Z_2 + Z_1}$$
The reflection loss in decibels quantifies how much of the incident wave is reflected:
$$\text{RL} = 20 \cdot \log_{10}|R| \text{ dB}$$
A large impedance mismatch (very different Z values) results in strong reflection and poor transmission. This is why sound transfers poorly between air (Z ≈ 413 rayl) and water (Z ≈ 1,480,000 rayl) — nearly all energy is reflected at the surface. Matching impedances (Z₁ ≈ Z₂) maximizes energy transfer, which is the principle behind impedance-matching layers in ultrasound transducers.
Air has an impedance of about 413 rayl, water approximately 1.48 × 10⁶ rayl, and steel about 4.7 × 10⁷ rayl. The reflection coefficient ranges from -1 to +1; a value near 0 indicates good impedance matching (minimal reflection), while values near ±1 indicate almost total reflection. The air-water interface has a reflection coefficient of about 0.9994, meaning only 0.06% of the energy transmits through — this is why underwater sound and airborne sound are almost completely isolated from each other.
Inputs
Results
Z₁(air) = 413 rayl, Z₂(water) = 1,477,040 rayl. R = 0.9994 — nearly total reflection. Sound crosses the air-water boundary extremely poorly.
Inputs
Results
Similar impedances yield R = 0.064 — only 0.4% of energy reflected. Well-matched materials transmit sound efficiently.
The rayl (named after Lord Rayleigh) is the unit of specific acoustic impedance, equal to Pa·s/m or kg/(m²·s). One rayl means that a pressure of 1 Pa produces a particle velocity of 1 m/s. Air has an impedance of about 413 rayl; water about 1.48 Mrayl; and steel about 47 Mrayl.
Medical ultrasound must transmit sound from the transducer (ceramic, Z ≈ 30 Mrayl) into body tissue (Z ≈ 1.6 Mrayl). Without matching layers, most energy would reflect at the interface. Impedance matching layers with intermediate Z values (geometric mean) maximize energy transfer, improving image quality and reducing required power.
When Z₁ = Z₂, the reflection coefficient R = 0 and the transmission coefficient T = 1. No sound is reflected — all energy passes through. This is the ideal case of perfect impedance matching.
Yes. When Z₂ < Z₁ (going from a dense to less dense medium), R is negative, meaning the reflected wave undergoes a 180° phase inversion. The magnitude of R still determines how much energy is reflected. For example, sound going from water into air has R ≈ -0.9994.
Temperature affects both density and sound speed. For air, density decreases and speed increases with temperature, but the net effect is small — impedance changes by roughly 0.1% per °C. For water, the effect is more complex due to the nonlinear behavior of water density with temperature.
Specific acoustic impedance (Z = ρc) is a property of the medium alone. Characteristic acoustic impedance additionally accounts for the geometry of the propagation path (e.g., in tubes and horns). In free-field conditions (open space), they are identical.
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