= Convected acoustic wave equation
{title2=$(\partial_t+U_0\partial_x)^2\rho_1=c_0^2\partial_x^2\rho_1$}
For a uniform background <velocity> $U_0$ and <speed of sound> $c_0$, linearized <conservation of mass>, the <Euler equation> and the local <equation of state> $p_1=c_0^2\rho_1$ give this <wave equation>. In the coordinate $x-U_0t$ it is the ordinary <one-dimensional wave equation>. Its two <characteristic curves> travel at laboratory <velocities> $U_0+c_0$ and $U_0-c_0$; both point downstream in <supersonic flow>.
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