A photograph 'depicts' its object. Is there a comparable verb for audio recordings?

Solution 1:

The verb depict can be defined as to represent, as a painting or picture does (that's from OED's definition for OP's context).

There is no "medium-specific" verb for representing something in an auditory, olfactory, gustatory, or tactile medium (songs, perfumes, statues, etc.). Figurative use, such as the song depicts [whatever it's supposed to "reflect, invoke"] is perfectly common. Otherwise, you can just use to represent in all contexts for all mediums.

The more "literal" general-purpose verbs include invoke, express, emulate, show, suggest, etc. Alternatives which are more "figurative" include reflect, capture, encapsulate, etc.

Solution 2:

Capture could cover both photographs and sound recordings.