Definitions of murmur:

noun: a schwa that is incidental to the pronunciation of a consonant
noun: a complaint uttered in a low and indistinct tone
noun: a low continuous indistinct sound; often accompanied by movement of the lips without the production of articulate speech
noun: an abnormal sound of the heart; sometimes a sign of abnormal function of the heart valves
verb: make complaining remarks or noises under one's breath
verb: speak softly or indistinctly
Example: "She murmured softly to the baby in her arms"