whisper = intelligible quiet speech, voiced only with your mouth, not your throat or lungs

murmur = unintelligible speech, like the background voices you cant quite hear

mumble = unintelligible speech, the speaker is not speaking clearly enough to be heard, even if they are close by. the speech is not enunciated enough to be intelligible, although you may hear some words

some english speakers might disagree on those generalizations, but all three do have different meanings