Acoustic Impedance Formula
Understand acoustic impedance (Z = ρv).
Includes specific acoustic impedance, reflection and transmission coefficients, and practical examples.
The Formula
Acoustic impedance (Z) measures how much resistance a medium offers to the passage of sound. It is the product of the medium's density (ρ) and the speed of sound in that medium (v). Just as electrical impedance governs how current flows in a circuit, acoustic impedance governs how sound energy transmits between materials.
When sound crosses the boundary between two materials with different impedances, some energy is reflected and some is transmitted. The greater the impedance mismatch, the more sound bounces back.
Variables
| Symbol | Meaning | Unit |
|---|---|---|
| Z | Specific acoustic impedance | Pa·s/m (rayl) |
| ρ | Density of the medium | kg/m³ |
| v | Speed of sound in the medium | m/s |
Reflection Coefficient Formula
The intensity reflection coefficient R tells you what fraction of sound energy is reflected at an interface. R = 0 means perfect transmission (no reflection). R = 1 means total reflection (no transmission). This formula is critical in designing acoustic barriers, medical ultrasound transducers, and noise control systems.
Example 1 — Acoustic Impedance of Air
Find the acoustic impedance of air at 20°C, where ρ = 1.21 kg/m³ and v = 343 m/s.
Z = 1.21 × 343
Z = 415 Pa·s/m
Example 2 — Acoustic Impedance of Water
Find the acoustic impedance of water, where ρ = 1000 kg/m³ and v = 1480 m/s.
Z = 1000 × 1480
Z = 1,480,000 Pa·s/m
This enormous mismatch between air (Z = 415) and water (Z = 1,480,000) explains why sound reflects so strongly at the water surface. It also explains why you can barely hear underwater sounds from above the surface — and vice versa.
Acoustic Impedance Reference Table
| Material | Density (ρ, kg/m³) | Speed of Sound (m/s) | Z (Pa·s/m) |
|---|---|---|---|
| Air (20°C) | 1.21 | 343 | 415 |
| Water (20°C) | 1,000 | 1,480 | 1,480,000 |
| Soft tissue (body) | 1,060 | 1,540 | 1,632,400 |
| Wood (pine) | 500 | 3,320 | 1,660,000 |
| Concrete | 2,300 | 3,100 | 7,130,000 |
| Steel | 7,800 | 5,100 | 39,780,000 |
Why Impedance Mismatch Matters
Sound travels most efficiently when impedances are matched. When they differ greatly, most of the energy is reflected rather than transmitted. This principle has far-reaching applications:
- Speaker design: Horn tweeters and bass ports are shaped to match the acoustic impedance of air and improve efficiency
- Room acoustics: Acoustic panels and diffusers work by creating impedance transitions that absorb or scatter sound
- Medical ultrasound: Gel is applied between the transducer and skin to eliminate the air gap, which would reflect nearly all the sound
- Underwater acoustics: Sonar systems account for the high impedance of water vs. sea floor sediment
- Noise barriers: Dense, heavy walls (high Z) reflect traffic noise rather than letting it pass through
When to Use It
Use the acoustic impedance formula when:
- Designing speaker enclosures, horns, or acoustic waveguides
- Predicting how much sound will pass through a wall, floor, or barrier
- Working on ultrasonic non-destructive testing (NDT) or medical imaging
- Calculating transmission loss at an air-water or air-solid boundary
- Building anechoic chambers or recording studios with precise acoustic control