= Solution
A <nondispersive wave> has a linear <dispersion relation> $\omega=vk$ over the relevant range, so every <Fourier transform> component has the same <phase velocity> $v_p=\omega/k=v$ and <group velocity> $v_g=d\omega/dk=v$. A <wave packet> then translates without spreading in an ideal homogeneous lossless medium.
For <wave dispersion>, $v_p$ depends on <frequency> or <wavenumber>. Different components accumulate different <phases>, and in general the <group velocity> differs from the <phase velocity>; variation of <group velocity> across the spectrum produces spreading of a <wave packet>. The membrane material can be nondispersive while confinement in a <membrane waveguide> introduces <wave dispersion> along its length.
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