Attenuation Within Domains
Rays can gradually lose energy as they propagate through absorbing media. For a plane wave propagating through an absorbing medium with attenuation coefficient α (SI unit: 1/m), the intensity decreases exponentially:
(8-3)
The Ray Acoustics interface defines an additional dependent variable A (dimensionless) for the path integral of the attenuation coefficient,
(8-4)
Despite requiring an extra degree of freedom per ray, the advantage of Equation 8-4 over Equation 8-3 is that the dependent variables in Equation 8-4 all vary linearly within a homogeneous medium. This makes Equation 8-4 much less prone to numerical stiffness; that is, it remains more accurate when the solver takes long time steps, compared to Equation 8-3, potentially reducing solution time and improving accuracy.
The attenuation coefficient is controlled by the option selected from the Fluid model list in the Pressure Acoustics Model section of the Medium Properties.
If Linear elastic is selected, no attenuation occurs.
If Linear elastic with attenuation is selected, the attenuation factor is user defined. Note that the attenuation coefficient α is a pressure amplitude attenuation coefficient in nepers per meter (Np/m). Alternatively, you can specify the amplitude attenuation coefficient in decibels per meter α’ or decibels per wavelength α(λ). Another option is to specify the intensity attenuation coefficient m directly. The relationships between these definitions of the attenuation coefficient may be summarized as follows:
If Thermally conducting and viscous is selected, the attenuation factor is defined in terms of the medium properties:
where
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c (SI unit: m/s) is the speed of sound in the medium,
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ρ (SI unit: kg/m3) is the density.
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Cp (SI unit:  J/(kg·K)) is the heat capacity at constant pressure.
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γ (dimensionless) is the ratio of specific heats.
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k (SI unit: W/(m·K)) is the thermal conductivity.
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μ (SI unit: Pa·s) is the dynamic viscosity.
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μB (SI unit: Pa·s) is the bulk viscosity.
Built-in models for attenuation in the ocean and atmosphere are also available. The theory for these features can be found in the Attenuation and Loss Models section in the Acoustic Properties of Fluids chapter.