Hi, Dr. Cox and Dr. Treeby,
I am confused about what's the meaning of c_0 in the equation of state in lossy media, which is:
p(r,t) = c_0(r)^2 * rho(r,t) + absp_term + disp_term
In lossy media, the sound speed depends on the frequency. In this case, what's the frequency does c_0 correspond to?
Thank you very much!
Best,
Chao
Hi Chao,
c_0 in the equation of state you give is the isentropic sound speed (sometimes called the thermodynamic sound speed). It's defined by c_0^2 = (dP / dRho), where P and Rho are the total pressure and density and the differential is evaluated at constant entropy. In a lossy medium, it's not this but the phase speed that depends on frequency. Given a dispersion relation defined with a complex wavenumber k, the phase speed is usually defined as c_p = w / k_real. In k-Wave, this dependence is modelled by the dispersion term.
I hope that helps. I think there's some information about c_0 and c_p for Stokes' equation in the chapter on absorption in Kinsler and Frey.
Brad.
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