Acoustic Wave Limit

35 Views Asked by At

I need a bit of help on how to proceed on this I need to derive the followinng:

$\frac{D^+}{Dt} (u+F) = 0$ and $\frac{D}{Dt} (u-F)= 0$, where $\frac{D^±}{Dt} = \frac{ \partial}{ \partial t} + (u ± c)\frac{ \partial}{ \partial x} $, the one dimensional wave equation in the acoustic limit

($u \ll c$ and $c \approx c_0 = \text{const.}$; $F = \frac{2c}{\gamma-1}$).