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In this paper it is shown that the state equation of Treeby and Cox [B. E.Treeby and B. T. Cox, J. Acoust. Soc. Am. \textbf{127} 5, (2010)] is\emph{nonlocal}, more precisely, a \emph{local} density variation causes an\emph{instant global} pressure variation and a \emph{local} pressure variationcan only be caused by an \emph{instant global} density variation. This is incontrast to all frequency dependent dissipative state equations known to theauthor. Moreover, it is shown that the Green function $G$ of the wave equationof Treeby and Cox cannot have a \emph{finite} wave front speed, i.e. thereexists no finite $c_F>0$ such that $$  G(\mathbf{x},t) = 0 \qquad\mbox{for}\qquad |\mathbf{x}|/c_F > t $$ holds,where $|\mathbf{x}|/c_F$ corresponds to the \emph{travel time} of a wavepropagating with speed $c_F$ from point $\mathbf{0}$ to point $\mathbf{x}$. Asa consequence, the density and pressure waves satisfying (i) the state equationof Treeby and Cox, (ii) the equation of motion and (iii) the equation ofcontinuity do not have a \emph{finite} wave front speed.

On the nonlocality of the state and wave equation of Treeby and Cox