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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?
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 unit is the Rayl (Pa·s/m or kg/m²·s). Large impedance mismatches between materials cause most sound energy to be reflected at the boundary rather than transmitted — this is why sound traveling from air to steel reflects almost entirely (≈99.99%).
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.
- Sonar Transducers — Quarter-wave matching layers are bonded to transducers to improve energy transfer between the piezoelectric crystal (high Z) and water (lower Z).
- 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.
- 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).
- Underwater Acoustics — The air-water interface reflects almost all sound, making ship noise detection from underwater difficult and vice versa.
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).