봐 is a shortened version of 보아. 보아's regular form is 보다. It means see, look at, and try something. In your question, 들어봐 and 느껴봐 's 봐 has the third meaning. So, each means try listening to it and try feeling it. Or just Listen to it and try to feel it. 소리봐 is incorrect. If you mean it 'Listen to it', it should be 들어봐. Other examples . 말해봐 = try to speak or try to tell. It is from 말하다 노래해봐 = try to sing. It is from 노래하다.

"봐" is short for "보아", and it's an imperative form of "보다(to look at, to see, to try + ing form)" In your example, it's used to mean "to try + ing form" meaning "verb stem + 아/어/여/해 봐". 느끼다(to feel) > 느끼 + 아/어/여/해 봐 > 느 + ㄲ + 여 봐 > 느껴봐(= Try feeling) 듣다(to hear) > 들 + 아/어/여/해 봐 > 들 + 어+봐 > (소리를) 들어봐(=Try hearing) \^o^/