Gravity affects anything with energy, including matter with mass (mass is a form of energy) but also light/electromagnetic waves/photons, which don’t have rest mass but do have energy and momentum. This is why light from distant galaxies can be bent and distorted during its travel from there to here — it is being affected by the warped spacetime aka gravity.
I don’t believe gravity directly affects sound waves. Like you said, it does affect the medium in which they travel, though, so for example a change in gravity can cause a change in the density of air and alter the properties of sound waves. It won’t make them fall down towards the source of gravity, though.
EDIT: According to the article shared by another commenter, this might be wrong, and sound waves may actually possess *negative* mass. Interesting!
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