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i am looking for a general form of a wave equation in a medium. i am not looking for a concrete physical equation but rather a generalized form (preferably in n dimension) of such under the simplest assumptions (it's of course a little equivocal what 'simplest' means but, well).

so for a scalar field ##\rho## a free wave equation is just

##\frac {\partial^2 \rho} {\partial t^2} - c^2 \nabla^2 \rho = 0##

but how does it look like in an inhomogeneous (but for now static) medium?

##\frac {\partial^2 \rho} {\partial t^2} - c(\vec x)^2 \nabla^2 \rho = 0##

like this?

and how does it look in the general case that the medium is time dependent with a flow ##\vec f(t, \vec x)##? basically where the speed of the wave becomes direction dependent. ##c## and ##\vec f## would have to be related via a continuity equation for the medium.