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Acoustic Impedance Calculator
Calculate the specific acoustic impedance Z = ρ × c for any medium, and find the reflection and transmission coefficients at the boundary between two materials.
Medium 1
kg/m³
m/s
Z₁ = ρ₁ × c₁
415 Pa·s/m
0.000415 MRayl
Medium 2
kg/m³
m/s
Z₂ = ρ₂ × c₂
1,481,000 Pa·s/m
1.481 MRayl
Boundary Results
Reflection Coefficient (R)
0.9994
pressure amplitude ratio
Transmission Coefficient (T)
0.0006
pressure amplitude ratio
Power Reflected
99.88 %
Power Transmitted
0.12 %
Transmission Loss
29.2 dB
Z Ratio (Z₂/Z₁)
3569×
Formulas
Z = ρ × c | R = (Z₂ − Z₁) / (Z₂ + Z₁) | T = 2Z₂ / (Z₁ + Z₂)
Power Reflection = R² | Power Transmission = 1 − R²
Acoustic Impedance of Common Materials
| Material | Density (kg/m³) | Speed (m/s) | Z (Pa·s/m = Rayl) | Z (MRayl) |
|---|---|---|---|---|
| Air (20°C) | 1.21 | 343 | 415 | 0.000415 |
| Fresh Water | 1000 | 1481 | 1,481,000 | 1.481 |
| Sea Water | 1025 | 1522 | 1,560,050 | 1.560 |
| Rubber | 1100 | 1600 | 1,760,000 | 1.76 |
| Concrete | 2300 | 3400 | 7,820,000 | 7.82 |
| Aluminum | 2700 | 6320 | 17,064,000 | 17.06 |
| Steel | 7800 | 5960 | 46,488,000 | 46.49 |
| Glass | 2500 | 5640 | 14,100,000 | 14.10 |
What is Acoustic Impedance?
This acoustic impedance calculator is built on a fundamental material property: specific acoustic impedance (Z) is the ratio of acoustic pressure to particle velocity in a medium. It quantifies how much a material resists the propagation of sound waves. Z = ρ × c, where ρ is the material density and c is the local speed of sound. The speed of sound itself depends on temperature and medium — you can calculate it for different conditions with the Speed of Sound Calculator.
The unit is the Rayl (Pa·s/m or kg/m²·s). Large impedance mismatch between materials governs both the sound reflection coefficient and the degree of acoustic transmission at a boundary — this is why sound traveling from air to steel reflects almost entirely (≈99.99%), with only a tiny fraction of power transmitted. The degree of this mismatch is captured by the Z ratio, shown in the Boundary Results panel above. Related phenomena such as standing waves inside cavities are driven by the same reflection physics — explore them with the Standing Wave Calculator.
Impedance Matching in Practice
- Medical Ultrasound — Gel is applied between the probe and skin to eliminate the large air-skin impedance mismatch. Without gel, virtually all ultrasound energy would reflect off the skin surface rather than entering the body. The same principle governs the frequency range a transducer can efficiently couple into tissue.
- Sonar Transducers — Quarter-wave matching layers are bonded to transducers to improve energy transfer between the piezoelectric crystal (high Z) and water (lower Z). The quarter-wavelength thickness is determined by the target operating frequency.
- Noise Barriers — Dense concrete walls have high acoustic impedance relative to air, causing very high reflection and significant transmission loss — effective at blocking airborne sound. The transmission loss in decibels is calculated directly from the power transmission coefficient (1 − R²).
- Loudspeaker Design — The air cavity, cone, and surround of a loudspeaker are carefully designed to maximize acoustic energy transfer from the moving cone (higher Z) to the surrounding air (very low Z). Poor impedance matching at the cone-air interface is a primary reason speaker efficiency is typically only 1–5%.
- Underwater Acoustics — The air-water interface reflects almost all sound, making ship noise detection from underwater difficult and vice versa. This same mismatch is exploited in anti-submarine barriers.
Frequently Asked Questions
What is the difference between acoustic impedance and specific acoustic impedance?
Specific acoustic impedance (Z = ρc) is a material property in units of Rayl (Pa·s/m). Acoustic impedance of a tube or duct (Z_a) is Z divided by the cross-sectional area (units: Pa·s/m³). This calculator computes specific acoustic impedance, which is the standard quantity for analyzing reflection and transmission at planar boundaries between materials.
Why does sound reflect almost entirely at an air-water boundary?
Water's impedance (≈1.48 MRayl) is about 3,570× greater than air's (≈415 Rayl). The power reflection coefficient is R² where R = (Z₂−Z₁)/(Z₂+Z₁) ≈ 0.9994, so about 99.88% of incident power reflects. Less than 0.12% transmits. This is why you can barely hear music playing at the bottom of a pool when standing outside, and vice versa.
How does impedance matching improve sound transmission?
Impedance matching places an intermediate layer with a Z between the two media. The optimal matching impedance is Z_match = √(Z₁ × Z₂), and the layer thickness should be a quarter-wavelength at the target frequency. This technique is used in medical ultrasound probes, sonar transducers, and anti-reflection coatings in optics (an analogous electromagnetic case).
What is the difference between Pa·s/m (Rayl) and MRayl?
One MRayl equals one million Rayl (Pa·s/m). Air's impedance (~415 Rayl) is more conveniently expressed in Rayl, while solid materials like steel (~46.5 MRayl) or aluminum (~17 MRayl) are typically quoted in MRayl. The calculator displays both units so you can match whichever convention appears in your textbook or datasheet. Ensure both materials use the same unit when computing the impedance ratio or reflection coefficient by hand.
Does the reflection coefficient formula assume normal incidence?
Yes. The formula R = (Z₂ − Z₁) / (Z₂ + Z₁) applies strictly to a plane wave hitting a flat boundary at normal (perpendicular) incidence. At oblique angles, Snell's law governs the refracted angle and the Fresnel-like pressure coefficients differ for each angle. For most engineering estimates — noise barriers, ultrasound coupling — normal-incidence results are a useful first approximation, but grazing-angle applications require the full angle-dependent treatment.
How does temperature affect acoustic impedance?
Temperature changes both density and the speed of sound, so it affects Z = ρ × c in both terms. In air, rising temperature lowers density but raises sound speed; the net effect is a slight increase in Z with temperature. In water, rising temperature lowers density and lowers sound speed slightly, reducing Z. For precise calculations at non-standard temperatures, enter the temperature-corrected density and sound speed in the Custom fields, or compute the sound speed first with the Speed of Sound Calculator.