= Wave propagation
<Wave propagation> is the evolution of a disturbance through space and <time> under the medium's dynamical equations. In a uniform nondispersive one-dimensional model,
$$
\partial_t^2u=c^2\partial_x^2u,
$$
the <wave equation> admits rightward and leftward profiles $u=f(x-ct)+g(x+ct)$. Each profile travels at <wave speed> $c$ without changing shape, so a measured delay over a known distance can determine $c$.
A real medium can alter this simple picture through <dispersion>, <wave absorption>, <wave reflection> and <wave scattering>. <Phase velocity> follows a fixed <wave phase>, while <group velocity> describes a narrowband <wave packet>'s envelope in a regime where that approximation holds. Neither should be identified automatically with every signal's arrival speed. Specifying an initial disturbance and suitable <boundary conditions> determines which of the possible propagation patterns occurs.
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