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In ocean acoustics the speed of sound $c$ can often include an imaginary component that accounts for attenuation due to the nature of the medium. That is, $c = c_r - ic_i$ with $c_r$ the regular sound speed and $c_i$ the attenuation. Jensen, et.al. 2011 elaborate on this expression in section 1.5.1 of their textbook.

Another definition of sound speed is $$c^2 = \frac{K}{\rho}$$ where $K$ is the fluid bulk modulus of the medium, and $\rho$ is the medium density.

Is the complex-valued sound speed meant to be compatible with this latter definition? Or is the complex-valued sound speed just another convenient way to include attenuation in the equations that it is involved in?

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    $\begingroup$ The textbook is Computational Ocean Acoustics (springer.com/us/book/9781441986771). And it appears to just be a convenient convention, where the imaginary part contains the information about the modulation (see Eq 1.43: $c_i \approx \delta c_r$). The local sound speed is still $c_r^2 \approx c_r^2 + c_i^2 = c^2 = K/\rho$, since $c_i \ll c_r$. $\endgroup$
    – Novice C
    Commented May 27, 2019 at 3:53

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The latter is compatible with former. In general, both bulk modulus can have an imaginary part (related to thermal losses) and density can have an imaginary part (related to viscous losses). In one or both are complex, the resulting sound speed will be complex.

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