Specific Acoustic Impedance

Overview

Engineering reference data for Specific Acoustic Impedance in acoustics.

Key Formulas

Speed of Sound

$c = \sqrt{\gamma R T}$

Speed of sound in an ideal gas.

Sound Level

$L = 10 \log_{10}(I/I_0)$

Decibel level.

Wavelength

$\lambda = c / f$

Wavelength = speed / frequency.

Variables

Physical Significance

Specific acoustic impedance (Z) quantifies the inherent resistance a medium offers to the propagation of sound. The relationship Z = ρc underscores that this property is determined solely by the medium's density (ρ) and the speed of sound (c) within it, not by the sound wave's characteristics. It defines the coupling between the sound pressure (p) and the resulting particle velocity (v).

Key Relationships & Properties

The fundamental formula relates impedance, pressure, and velocity: $Z = \frac{p}{v} = \rho c$

For a plane wave traveling through a medium, the specific acoustic impedance is a real number. In more complex scenarios involving viscous or reactive media, it can be a complex quantity: $Z = R + iX$ where R is the resistive (real) part and X is the reactive (imaginary) part.

The impedance is also related to the medium's bulk modulus (K) through the relationship: $c = \sqrt{\frac{K}{\rho}} \quad \Rightarrow \quad Z = \rho \sqrt{\frac{K}{\rho}} = \sqrt{\rho K}$

Impedance Mismatch and Acoustic Effects

A critical concept is the impedance mismatch at the boundary between two media with different specific acoustic impedances (Z₁ and Z₂). This mismatch governs the reflection and transmission of sound energy.

• Reflection Coefficient (R): $R = \frac{Z_2 - Z_1}{Z_2 + Z_1}$
• Transmission Coefficient (T): $T = \frac{2 Z_2}{Z_2 + Z_1}$

A large difference between Z₁ and Z₂ results in strong reflection, which is why air (Z ≈ 415 Pa·s/m) and water (Z ≈ 1.5 × 10⁶ Pa·s/m) are nearly perfect reflectors of sound at their interface.

Representative Values

The table below provides orders of magnitude for common materials at standard conditions.

Interactive Charts

References

• Original Source