Acoustic Impedance Calculator – Reflection & Transmission Coefficients
Calculate acoustic impedance, reflection, and transmission coefficients for sound waves
Select the calculation type, then enter the material densities and sound speeds to compute acoustic impedance, reflection coefficient, and transmission coefficient.
Acoustic Impedance Calculator – Reflection & Transmission Coefficients
Calculate acoustic impedance, reflection, and transmission coefficients for sound waves
About the Acoustic Impedance Calculator
Acoustic impedance is a fundamental property that governs how sound waves behave at the boundary between two different materials. Just as electrical impedance determines how current flows in a circuit, acoustic impedance determines how sound energy propagates through a medium and what happens when sound encounters a change in material properties.
The acoustic impedance of a medium is defined as Z = ρ × c, where ρ is the density of the medium in kilograms per cubic metre and c is the speed of sound in that medium in metres per second. The result is expressed in Rayleigh (Rayl), with 1 Rayl = 1 Pa·s/m = 1 kg/(m²·s). Denser and stiffer materials generally have higher acoustic impedance: steel (≈47 MRayl) has orders of magnitude more impedance than air (≈420 Rayl).
When a sound wave reaches the interface between two media with different acoustic impedances, part of the wave is reflected and part is transmitted. The fraction reflected and transmitted depends entirely on the impedance mismatch. The pressure reflection coefficient is R = (Z₂ − Z₁) / (Z₂ + Z₁), and the pressure transmission coefficient is T = 2Z₂ / (Z₂ + Z₁). The intensity reflection coefficient is R², and transmitted intensity is 1 − R², so energy is always conserved at the interface.
In medical imaging, this principle is central to ultrasound diagnostics. The transducer emits sound pulses that reflect at tissue boundaries with different impedances — the echoes are measured to construct images. The large impedance mismatch between soft tissue (≈1.5 MRayl) and air (≈420 Rayl) means any air pocket between the probe and skin would reflect virtually all the sound, which is why a coupling gel is essential. Similarly, the mismatch between soft tissue and bone (≈7 MRayl) creates strong reflections that limit ultrasound imaging of structures behind bone.
In industrial applications, acoustic impedance matching is critical for non-destructive testing (NDT). Ultrasonic probes must be acoustically coupled to metal components to detect internal flaws. In sonar, acoustic impedance contrasts between water and submarine hulls or the seabed determine detection performance. This calculator provides the acoustic impedances of individual media and the reflection/transmission coefficients at their interface, making it useful for acoustics design, materials analysis, and educational physics work.
Acoustic Impedance Examples
These examples show acoustic impedance and reflection calculations for common material interfaces.
| Interface | Key Results | Notes |
|---|---|---|
| Water (ρ = 1000 kg/m³, c = 1480 m/s) → Air (ρ = 1.225 kg/m³, c = 343 m/s) | Z₁ = 1.48 MRayl, Z₂ = 420 Rayl, R ≈ −0.9994, T_intensity ≈ 0.12% | Almost total reflection at the water–air interface. This is why ultrasound gel is needed in medical imaging — air pockets would reflect nearly all the sound energy. |
| Steel (ρ = 7850 kg/m³, c = 5960 m/s) → Water (ρ = 1000 kg/m³, c = 1480 m/s) | Z₁ ≈ 46.79 MRayl, Z₂ = 1.48 MRayl, R ≈ −0.939, T_intensity ≈ 11.8% | Most sound is reflected at the steel–water interface. The negative R indicates a phase inversion (going from high- to low-impedance medium). Only about 12% of sound intensity is transmitted, making this interface important in underwater acoustics and non-destructive testing. |
| Aluminium (ρ = 2700 kg/m³, c = 6420 m/s) | Z = 17.334 MRayl | Characteristic acoustic impedance of aluminium. High impedance materials like metals are efficient sound conductors compared to low-impedance materials like air or foam. |
| Bone (ρ = 1900 kg/m³, c = 4080 m/s) | Z = 7.752 MRayl | Acoustic impedance of cortical bone, relevant in medical ultrasound and lithotripsy. The significant mismatch between bone and soft tissue causes partial reflection at tissue–bone interfaces. |
How to use the Acoustic Impedance Calculator
- Select the calculation type: 'Reflection & Transmission' to analyse a boundary between two media, or 'Acoustic Impedance Only' to compute Z for a single medium.
- Enter the density of Medium 1 (ρ₁) in kg/m³ and the sound speed in Medium 1 (c₁) in m/s.
- For reflection/transmission calculations, also enter the density and sound speed of Medium 2.
- Click Calculate to obtain acoustic impedances in Rayleigh (Pa·s/m), the pressure reflection and transmission coefficients, and the percentage of intensity reflected and transmitted.
- Use the example buttons to quickly load common material pairings such as water–air or steel–water.
Acoustic Impedance FAQ
What is acoustic impedance?
Acoustic impedance (Z) is the resistance a medium offers to the propagation of sound waves. It is defined as Z = ρ × c, where ρ is the density of the medium in kg/m³ and c is the speed of sound in that medium in m/s. The unit is the Rayleigh (Rayl), equal to 1 Pa·s/m or 1 kg/(m²·s). A high acoustic impedance means the medium transmits sound pressure efficiently but resists flow; a low impedance means the opposite.
How is the reflection coefficient calculated?
The pressure reflection coefficient R = (Z₂ − Z₁) / (Z₂ + Z₁), where Z₁ and Z₂ are the acoustic impedances of the first and second medium, respectively. R ranges from −1 to +1. A negative R means the reflected wave is phase-inverted (denser to less dense). The intensity reflection coefficient is R² × 100%, giving the percentage of incoming sound energy that is reflected.
What is the transmission coefficient?
The pressure transmission coefficient T = 2Z₂ / (Z₂ + Z₁). It represents the ratio of the transmitted pressure amplitude to the incident pressure amplitude. The intensity transmission coefficient is 1 − R² (or equivalently 4Z₁Z₂ / (Z₁+Z₂)²), giving the percentage of incoming energy that passes through the interface. Note that T can exceed 1 (the pressure amplitude can increase), but the intensity is always conserved: reflected intensity + transmitted intensity = 100%.
Why is acoustic impedance matching important in medical ultrasound?
In medical ultrasound, the sound beam must pass from the transducer through coupling gel, skin, soft tissue, and potentially bone. Large impedance mismatches cause strong reflections that prevent imaging of deeper structures. Ultrasound coupling gel has an acoustic impedance close to soft tissue (~1.5 MRayl), eliminating the large air gap that would otherwise reflect nearly all the sound. In ultrasound therapy and lithotripsy, impedance matching ensures sufficient energy is delivered to the target tissue.
What are typical acoustic impedances of common materials?
Air has Z ≈ 420 Rayl (at 20°C), making it a very poor acoustic conductor. Fresh water has Z ≈ 1.48 MRayl, and soft tissue is similar at 1.5–1.65 MRayl. Bone ranges from 6–8 MRayl, making it a significant reflector. Metals are much denser: steel ≈ 47 MRayl, aluminium ≈ 17 MRayl, and copper ≈ 41 MRayl. These large contrasts mean nearly all sound is reflected at metal–air interfaces, which is why ultrasonic non-destructive testing requires couplant gels.
What are some practical applications of acoustic impedance calculations?
Acoustic impedance calculations are used in medical ultrasound imaging and therapy, sonar systems, non-destructive testing (NDT) of materials and welds, architectural acoustics for designing echo-free spaces, loudspeaker and microphone design, underwater acoustics for submarine detection, and seismology for analysing how seismic waves reflect at geological boundaries. In each case, understanding the impedance mismatch at boundaries helps engineers predict how much sound energy will be reflected versus transmitted.