We consider a model time-harmonic wave equation of acoustic tomography of moving fluid in an open bounded domain in $\mathbb R^d$, $d \geq 2$, with variable sound speed $c$, density $\rho$, fluid velocity $v$ and absorption coefficient $\alpha$. We give global uniqueness results for related inverse boundary value problem for the cases of boundary measurements given for two and for three fixed frequencies. Besides, we also give a non-uniqueness result for this inverse problem for the case of boundary measurements given for all frequencies.