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. For inhomogeneous 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.

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:

where ${\displaystyle \omega }$ is the angular frequency, P the pressure, ${\displaystyle \Delta x}$ the wave propagation distance, ${\displaystyle \alpha (\omega )}$ the attenuation coefficient, ${\displaystyle \alpha _{0}}$ and frequency dependent exponent ${\displaystyle \eta }$ are real non-negative material parameters obtained by fitting experimental data and the value of ${\displaystyle \eta }$ ranges from 0 to 2. Acoustic attenuation in water, many metals and crystalline materials are frequency-squared dependent, namely ${\displaystyle \eta =2}$. In contrast, it is widely noted that the frequency dependent exponent ${\displaystyle \eta }$ of viscoelastic materials is between 0 and 2. For example, the exponent ${\displaystyle \eta }$ of sediment, soil and rock is about 1, and the exponent ${\displaystyle \eta }$ of most soft tissues is between 1 and 2.

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