About

Acoustic impedance Z determines how sound energy transfers between materials. A mismatch between two media causes partial reflection at the boundary. In medical ultrasound, a transducer-tissue mismatch of even 5% degrades image resolution. In non-destructive testing (NDT), selecting the wrong couplant material means defects go undetected. This calculator computes specific acoustic impedance from density ρ and longitudinal sound velocity c, then derives reflection (R) and transmission (T) coefficients at any two-material interface.

Results are expressed in Rayl (1 Rayl = 1 Pa⋅s/m) or MRayl for solids. The model assumes plane-wave propagation at normal incidence. It does not account for shear waves, attenuation, or oblique incidence angles governed by Snell's law. For layered composites or frequency-dependent media, treat these values as first-order approximations.

Formulas

Specific acoustic impedance for a homogeneous medium under plane-wave assumption:

Z = ρ × c

where Z = specific acoustic impedance Pa⋅s/m (Rayl), ρ = material density kg/m³, c = longitudinal speed of sound m/s.

Pressure reflection coefficient at normal incidence between medium 1 and medium 2:

R = Z₂ − Z₁Z₂ + Z₁

Pressure transmission coefficient:

T = 2Z₂Z₂ + Z₁

Intensity reflection coefficient:

R_I = R² = (Z₂ − Z₁Z₂ + Z₁)²

Intensity transmission coefficient:

T_I = 1 − R_I

where R ranges from −1 to +1 and T ranges from 0 to 2. A negative R indicates a phase inversion upon reflection (when Z₂ < Z₁).

Reference Data

Material	Density ρ kg/m³	Sound Velocity c m/s	Impedance Z MRayl
Air (20 °C)	1.204	343	0.000413
Water (20 °C)	998	1482	1.48
Seawater (25 °C)	1025	1531	1.57
Human Soft Tissue	1060	1540	1.63
Blood	1060	1570	1.66
Fat	920	1450	1.33
Bone (Cortical)	1900	4080	7.75
Liver	1060	1590	1.69
Muscle	1050	1580	1.66
Lung (Inflated)	400	650	0.26
PMMA (Perspex)	1180	2730	3.22
Polystyrene	1060	2340	2.48
PZT Ceramic (PZT-5A)	7750	4350	33.71
Aluminium	2700	6320	17.06
Steel (Mild)	7850	5960	46.79
Stainless Steel 304	8000	5790	46.32
Titanium	4507	6070	27.36
Copper	8960	4660	41.75
Glass (Pyrex)	2230	5640	12.58
Quartz (Fused)	2200	5930	13.05
Concrete	2300	3100	7.13
Rubber (Silicone)	1100	1000	1.10
Glycerin	1260	1920	2.42
Mercury	13546	1450	19.64
Lead	11340	2160	24.49

Frequently Asked Questions

Both density ρ and sound velocity c are temperature-dependent. In water, c increases from 1482 m/s at 20°C to 1529 m/s at 40°C, while density drops slightly. In gases, c scales with √T (absolute temperature). For precise NDT work, always measure or look up material properties at your operating temperature.

For plane waves in a lossless medium, specific acoustic impedance and characteristic impedance are identical: Z = ρc. The distinction arises in waveguides and ducts where geometry affects impedance. This calculator computes specific (characteristic) impedance, valid for unbounded or far-field conditions.

A negative pressure reflection coefficient R occurs when the second medium has lower impedance than the first (Z₂ < Z₁). This means the reflected pressure wave undergoes a 180° phase inversion. The intensity reflection coefficient R_I = R² is always positive since energy has no phase.

No. The formulas assume normal incidence (angle = 0°). At oblique angles, Snell's law applies and the reflection coefficient becomes angle-dependent. For critical angle analysis or mode conversion (longitudinal to shear), a more complex model incorporating θ is required.

Convention uses MRayl (10⁶ Pa⋅s/m) for solids and dense liquids. Soft tissue typically falls between 1.3 and 1.7 MRayl. Air is approximately 413 Rayl (0.000413 MRayl). The calculator displays both units.

Enter the impedance of your transducer face (e.g., PZT ceramic at 33.7 MRayl) as Material 1 and the test piece as Material 2. Then check the intensity reflection coefficient R_I. A good couplant (like glycerin or specialized gels) should minimize R_I at each interface. In practice, matching layers are designed with impedance Z_match = √Z₁ × Z₂.