What Is Acoustic Impedance?
Our acoustic impedance calculator helps you find the specific acoustic impedance of a material (z) and determine the intensity coefficients of reflection and transmission of a sound wave at the boundary between two materials. The wide range of applications of acoustic impedance — from ultrasound imaging and tympanometry to architectural acoustics, soundproofing, and aeronautical noise control — makes it an important property.
If we played a sound from the same source in a room filled with air and then underwater in a pool, would it behave the same? 🤔 Sound is a wave of pressure that requires a medium to propagate, and the properties of each material affect the speed and intensity of the wave.
The speed of sound in a given medium (gas, liquid, or solid) depends primarily upon how compressible it is. In solids and liquids — which are less compressible than gases and have a higher modulus of elasticity — the speed of sound is faster.
The acoustic impedance (Z) is a property that affects how sound travels through a material. It represents the medium's resistance to the propagation of sound, affecting its intensity. The higher the value of Z, the greater the opposition to the transmission of the sound.
The acoustic impedance (Z) is particular to a geometry and a material, and is given by the ratio of the wave's acoustic pressure to flow. Similarly, the specific acoustic impedance (z) is an intensive material property that relates the wave's pressure to the medium's particle velocity.
Specific Acoustic Impedance Formula
For plane waves, the specific acoustic impedance is expressed in terms of the density of the medium (ρ) and the speed of the sound wave in that material (c):
z = ρ × c
Where:
- z — specific acoustic impedance, measured in rayls (1 Rayl = 1 Pa·s/m = 1 kg·m⁻²·s⁻¹). Values are often quoted in MRayl (10⁶ Rayl).
- ρ — density of the medium (kg/m³ in metric, lb/ft³ in the American system).
- c — speed of sound in the material (m/s or ft/s).
Using the formula, let's compare the z of water and air at the same temperature:
- Water, with a density of 1000 kg/m³ and a speed of sound of 1480 m/s, has a z of 1.48 MRayl.
- Air, with a density of 1.225 kg/m³ and a speed of sound of 343 m/s, has a z of 0.00042 MRayl.
Notice that even though sound moves about 4.3 times faster in water than in air, the specific acoustic impedance of air is roughly 3,700 times smaller than that of water — which is why so little sound energy crosses the air–water boundary.
Intensity Reflection and Transmission Coefficients
When a sound wave traveling in a medium of impedance z₁ hits the boundary of a second medium of impedance z₂ at normal incidence, part of its energy is reflected and part is transmitted. The intensity reflection coefficient (R) and transmission coefficient (T) are:
R = ((z₂ − z₁) / (z₂ + z₁))²
T = 1 − R = 4·z₁·z₂ / (z₁ + z₂)²
Because energy is conserved, R + T = 1 (100%). Key insights:
- When the two impedances are equal (z₁ = z₂), R = 0 and T = 1 — all the sound is transmitted. This is called impedance matching.
- When the impedances are very different (e.g., air to water), almost all the energy is reflected. This is why ultrasound gel is used to match the probe to the skin.
Specific Acoustic Impedance of Some Materials
| Material | Density ρ (kg/m³) | Speed c (m/s) | z (MRayl) |
|---|---|---|---|
| Air (20°C) | 1.225 | 343 | 0.0004 |
| Water (20°C) | 1,000 | 1,480 | 1.48 |
| Seawater | 1,027 | 1,500 | 1.54 |
| Blood | 1,060 | 1,570 | 1.66 |
| Soft Tissue | 1,043 | 1,540 | 1.61 |
| Fat | 952 | 1,450 | 1.38 |
| Muscle | 1,065 | 1,580 | 1.68 |
| Bone (cortical) | 1,912 | 4,080 | 7.80 |
| Brain | 1,030 | 1,550 | 1.60 |
| Rubber | 1,100 | 1,600 | 1.76 |
| Wood (oak) | 720 | 3,850 | 2.77 |
| Concrete | 2,300 | 3,400 | 7.82 |
| Glass | 2,500 | 5,640 | 14.10 |
| Aluminum | 2,700 | 6,420 | 17.33 |
| Steel | 7,800 | 5,900 | 46.02 |
| Copper | 8,930 | 4,660 | 41.61 |
| Gold | 19,320 | 3,240 | 62.60 |
How to Use the Acoustic Impedance Calculator
- Select what to calculate — Choose Specific Acoustic Impedance (z) for a single material, or Reflection & Transmission to analyze a boundary between two materials.
- Choose a unit system — Metric (kg/m³, m/s) or American/Imperial (lb/ft³, ft/s).
- Pick the material(s) — Select from the preset list (air, water, tissue, bone, metals, etc.) or choose Custom to enter your own density and speed of sound.
- Click Calculate — The result appears instantly: the specific acoustic impedance in MRayl and Rayl, or the reflection and transmission coefficients with a visual breakdown and the formula used.
FAQs
- What units is acoustic impedance measured in?
- The SI unit is the rayl: 1 Rayl = 1 Pa·s/m = 1 kg·m⁻²·s⁻¹. In practice, values are usually given in MRayl (mega-rayls, 10⁶ Rayl). There is also a CGS rayl, where 1 CGS rayl = 10 SI rayls.
- Why is acoustic impedance important in ultrasound?
- Ultrasound images are formed by echoes from boundaries between tissues of different acoustic impedance. The larger the impedance mismatch, the stronger the reflection — which is why a coupling gel is used to eliminate the air gap between the probe and the skin.
- What is impedance matching?
- When two media have the same acoustic impedance, no sound is reflected at their boundary (R = 0) and all of it is transmitted (T = 1). Matching layers are used in transducers and loudspeakers to maximize energy transfer.
- Why does so little sound pass from air into water?
- The acoustic impedance of water is about 3,500–3,700 times larger than that of air. This huge mismatch reflects more than 99.9% of the incident sound energy, so very little is transmitted across the surface.
- What is the difference between Z and z?
- The acoustic impedance Z depends on both the material and the geometry (it relates pressure to volume flow). The specific acoustic impedance z is an intensive material property (pressure to particle velocity) and equals ρ × c for a plane wave.