Acoustic Impedance Calculator

Acoustic Impedance — Deep Dive (What It Means & Why It Matters)

Acoustic impedance connects sound pressure to particle velocity. For a uniform, lossless medium the characteristic (specific) impedance is \( z = \rho\,c \) with units Rayl \(=\text{Pa·s/m}\), where \( \rho \) is density and \( c \) is the speed of sound. Intuitively, higher \( z \) means the medium resists particle motion more for a given pressure fluctuation. Air has a low impedance (hundreds of Rayl), water and soft tissue are much higher (about 1–2 MRayl), and metals are higher still (tens of MRayl).

In tubes or ducts that carry plane waves, we often speak about the tube characteristic impedance \( Z_c = \rho c / S \) (Pa·s/m³), which incorporates cross-sectional area \( S \). This tells you how “hard” it is for a source to drive volume flow in that geometry; narrowing the tube increases \( Z_c \) even if the medium is unchanged.

Interfaces, Reflections, and Transmission

When a plane wave hits a flat boundary at normal incidence, differences in impedance control how much sound is reflected. The pressure reflection coefficient is \( r = \dfrac{z_2 - z_1}{z_2 + z_1} \). The corresponding intensity (power) reflection and transmission are \( R = |r|^2 \) and \( T = \dfrac{4 z_1 z_2}{(z_1 + z_2)^2} \) with \( R+T=1 \) in lossless cases. A huge mismatch (e.g., water–air) yields \( R \approx 1 \): almost everything reflects. This is why underwater sounds couple so poorly into air, and why matching layers (materials whose impedance sits between source and load) are used in ultrasound transducers and microphones.

Frequency, Wavelength, and Loss

Wavelength follows \( \lambda = c/f \). In air at 20 °C where \( c \approx 343\,\text{m/s} \), a 1 kHz tone has \( \lambda \approx 0.343\,\text{m} \). In reality, media have absorption and viscosity; a simple way to express this is a complex impedance, e.g., \( z^\* = \rho c\,\sqrt{1 + i\eta} \) with a small loss term \( \eta \). For most everyday calculations the lossless form \( z=\rho c \) is a good first approximation.

Point, Radiation, and Practical Sources

For loudspeakers, horns, and vibrating pistons, the relevant quantity is often the radiation impedance seen by the source, which combines the medium’s characteristic impedance with geometry-dependent effects (baffling, aperture size, frequency). Horns and quarter-wave transformers “step” impedance gradually to improve power transfer, just as in RF transmission lines.

Typical Ballpark Values (Order-of-Magnitude)

• Air (20 °C): \( z \approx 4.1 \times 10^2 \) Rayl
• Freshwater: \( z \approx 1.48 \times 10^6 \) Rayl (1.48 MRayl)
• Soft tissue (ultrasound): ~1.6 MRayl
• Aluminum: ~17 MRayl (frequency-dependent effective values in solids)

When to Go Beyond the Simple Model

Use the simple formulas for plane waves, small signal levels, and broad planning. For precision work (medical ultrasound, sonar, high-temperature gases, deep-ocean conditions, porous/foams, or oblique incidence), you’ll need frequency-dependent material data, angle-dependent boundary conditions, and possibly layering models (quarter-wave stacks). Always validate assumptions against your application and measurement environment.