There is a third meaning: to taste.
Examples:
1a. senti se ti piace questa cioccolata.
or:
1b. assaggia questa cioccolata e dimmi se ti piace
As you can see the sentence with /sentire/ is shorter and actually will be used much more often.
- senti se la pasta e` cotta
- hai sentito che buona questa lasagna?
In my experience I never had any problems with those possible multiple meanings
as the context always guided me.
I remember an advertisement about a brand of wine, where the image of the bottle
was near the ear of a 'feeler'.
That was just advertising the state of mental confusion that alcohol might produce,
and it was exactly done with the double meaning 'to hear', 'to taste'.
I dislike advertisement, but honestly that was well done.
In my view the lack of distinction intrinsic to the word 'nipote' (double meaning also here) is,
for another example, something that sometimes causes greater problems.