Is there a comparable word to 'visibility' for hearing?

Solution 1:

I think you are looking for audibility:

• quality or fact or degree of being audible or perceptible by the ear

The Free Dictionary

"Hearing range":

• usually describes the range of frequencies that can be heard by humans or other animals, though it can also refer to the range of levels. The human range is commonly given as 20 to 20,000 Hz. (Wikipedia)

Solution 2:

While audibility is certainly the most precise term as Josh61 suggests, I believe clarity or clear finds more common usage in description of audio quality or sound perceptibility. For example, "I hear you loud and clear" is a common way to confirm that someone's speech was understood.