= Solution
<Wave dispersion> means that different <frequencies> propagate with different <phase velocities>, so a <wave packet> generally changes shape. Equivalently the <dispersion relation> is not proportional to $k$ over the relevant band. Three natural examples are the colour separation in a <rainbow>, where the refractive index of water depends on <wavelength>; deep-water <surface gravity waves>, for which $\omega^2=gk$ and long waves have larger <phase velocity>; and <capillary waves>, whose short-wave limit is $\omega^2=(\gamma/\rho)k^3$ and whose shorter waves have larger <phase velocity>. Here $g$ is <gravitational acceleration>, $\gamma$ is <surface tension>, and $\rho$ is fluid <mass density>, with positive $k$ and negligible viscosity.
A distinct application is an <optical prism> <spectrometer>: the wavelength-dependent <refractive index> produces different <refraction> angles, separating spectral components for measurement. This exploits <wave dispersion> deliberately.
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