Remove silence from audio in javascript

Question

I want to create a web application in javascript where the user records voice recording from a microphone, and then the application mutes the quiet part of the recording, so just the voice remains. Please note that the quiet parts may not be completely silent because the sound is recorded from the microphone, so there may be some background noise. But this noise will, however, be much quieter than speech.

I need to be guided by how to do this. Some example of something like this would be nice. If not in javascript than in any language, just so that I can understand.

EDIT: I already processed the recording part using the web audio API. I just need help with pruning.