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Consider the following information:

Waves - whether they are sound or light or water - are local phenomena, which means how the wave decides to move is determined by its immediate surroundings, not by whatever the source may have been doing far away. The speed of the source affects the frequency of the wave, but two waves of the same frequency in the same medium will move at the same speed, which for light in air is, as you said, a bit slower than $c$.

The quote above was found in a post related to special relativity and the constancy of speed of light, for context. However, it seems to imply that wave frequency affects wave velocity.

I thought these were independent. In fact, it's easy to find articles asserting that wave frequency doesn't affect its velocity.

So: can wave frequency in fact influence its velocity in a medium?

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can wave frequency in fact influence its velocity in a medium?

Yes. This phenomenon is called dispersion and media in which dispersion occurs are called dispersive. Dispersion can lead to all sorts of interesting effects, including most familiarly the production of rainbows.

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