Acoustic attenuation

Acoustic attenuation is a measure of the energy loss of sound propagation in media. Most media have viscosity and are therefore not ideal media. When sound propagates in such media, there is always thermal consumption of energy caused by viscosity. This effect can be quantified through the Stokes's law of sound attenuation. Sound attenuation may also be a result of heat conductivity in the media as has been shown by G. Kirchhoff in 1868. The Stokes-Kirchhoff attenuation formula takes into account both viscosity and thermal conductivity effects.

For heterogeneous media, besides media viscosity, acoustic scattering is another main reason for removal of acoustic energy. Acoustic attenuation in a lossy medium plays an important role in many scientific researches and engineering fields, such as medical ultrasonography, vibration and noise reduction.

Power-law frequency-dependent acoustic attenuation

Many experimental and field measurements show that the acoustic attenuation coefficient of a wide range of viscoelastic materials, such as soft tissue, polymers, soil, and porous rock, can be expressed as the following power law with respect to frequency:

:$P(x+\Delta x)=P(x)e^, \alpha(\omega)=\alpha_0\omega^\eta$

where $\omega$ is the angular frequency, ''P'' the pressure, $\Delta x$ the wave propagation distance, $\alpha (\omega)$ the attenuation coefficient, and $\alpha_0$ and the frequency-dependent exponent $\eta$ are real non-negative material parameters obtained by fitting experimental data; the value of $\eta$ ranges from 0 to 4. Acoustic attenuation in water is frequency-squared dependent, namely $\eta=2$. Acoustic attenuation in many metals and crystalline materials is frequency-independent, namely $\eta=1$. = 0.}

See also and the references therein.

Such fractional derivative models are linked to the commonly recognized hypothesis that multiple relaxation phenomena (see Nachman et al.) give rise to the attenuation measured in complex media. This link is further described in and in the survey paper.

For frequency band-limited waves, Ref. describes a model-based method to attain causal power-law attenuation using a set of discrete relaxation mechanisms within the Nachman et al. framework.

In porous fluid-saturated sedimentary rocks, such as sandstone, acoustic attenuation is primarily caused by the wave-induced flow of the pore fluid relative to the solid frame, with $\eta$ varying between 0.5 and 1.5.

See also

* Absorption (acoustics)
* Fractional calculus

References

{{Authority control

Sound measurements
Acoustics
Sound