Acoustic Impedance Calculator

Calculate impedance, reflection, and transmission coefficients.

Select the calculation type and enter the material properties below to get the results.

Examples

Explore common scenarios for calculating acoustic impedance.

Water to Air

impedance

Calculate the reflection and transmission when sound travels from water to air.

Density 1: 1000 kg/m³

Sound Speed 1: 1480 m/s

Density 2: 1.225 kg/m³

Sound Speed 2: 343 m/s

Steel to Water

impedance

An example of sound moving from a dense solid (steel) to a liquid (water).

Density 1: 7850 kg/m³

Sound Speed 1: 5960 m/s

Density 2: 1000 kg/m³

Sound Speed 2: 1480 m/s

Single Medium: Aluminum

impedance

Calculate the characteristic acoustic impedance of Aluminum.

Density 1: 2700 kg/m³

Sound Speed 1: 6420 m/s

Single Medium: Bone

impedance

Calculate the characteristic acoustic impedance of human bone, relevant in medical ultrasound.

Density 1: 1900 kg/m³

Sound Speed 1: 4080 m/s

Other Titles
Understanding Acoustic Impedance: A Comprehensive Guide
Learn the fundamentals of acoustic impedance and its importance in physics and engineering.

What is Acoustic Impedance?

  • Defining the Concept
  • The Formula Explained
  • Units of Measurement
Acoustic impedance (Z) is a physical property of a medium that describes how much resistance an acoustic wave encounters when propagating through it. It is analogous to electrical impedance in circuits. A high acoustic impedance indicates that a large pressure is required to produce a certain particle velocity, while a low impedance means a smaller pressure is needed for the same velocity.
The Core Formula
The characteristic acoustic impedance is calculated as the product of the medium's density (ρ) and the speed of sound (c) within that medium. The formula is: Z = ρ * c.

Step-by-Step Guide to Using the Calculator

  • Single Medium Calculation
  • Two Media Calculation
  • Interpreting the Results
Our calculator simplifies the process. For a single medium, just input its density and the speed of sound to find its impedance. For two media, provide the properties for both to get their respective impedances, plus the reflection and transmission coefficients at their boundary.

Real-World Applications of Acoustic Impedance

  • Medical Ultrasound Imaging
  • Architectural Acoustics
  • Geophysical Exploration
The concept is crucial in medical ultrasonography, where differences in the acoustic impedance of tissues create reflections that form an image. In architecture, it helps in designing soundproof rooms. Geologists use it to study earth layers by analyzing seismic wave reflections.

Reflection and Transmission at Boundaries

  • Understanding the Coefficients
  • The Role of Impedance Mismatch
  • Energy Conservation
When a sound wave hits a boundary between two media with different impedances (Z₁ and Z₂), part of the wave reflects, and part is transmitted. The greater the impedance mismatch, the more energy is reflected. The reflection coefficient (R) and transmission coefficient (T) quantify these effects, and their sum is always 1, signifying conservation of energy.
Formulas for Coefficients
Reflection Coefficient (R) = ((Z₂ - Z₁) / (Z₂ + Z₁))². Transmission Coefficient (T) = 1 - R.

Mathematical Derivation and Examples

  • Deriving the Impedance Formula
  • Sample Calculation Walkthrough
  • Common Material Values
Acoustic impedance is derived from the relationship between acoustic pressure (p) and particle velocity (u), where Z = p/u. By substituting fundamental wave equations, we arrive at Z = ρc. For example, the impedance of water (ρ ≈ 1000 kg/m³, c ≈ 1480 m/s) is approximately 1.48 x 10⁶ Rayl.