Yours, Etc.: Origins and Uses of 8 Sign-Offs
late 14c., "expression of discontent by grumbling," from Old French murmure "murmur, sound of human voices; trouble, argument" (12c.), noun of action from murmurer "to murmur," from Latin murmurare "to murmur, mutter," from murmur (n.) "a hum, muttering, rushing," probably from a PIE reduplicative base *mor-mor, of imitative origin (cf. Sanskrit murmurah "crackling fire," Greek mormyrein "to roar, boil," Lithuanian murmlenti "to murmur"). Meaning "softly spoken words" is from 1670s.
murmur mur·mur (mûr'mər)
An abnormal sound heard on auscultation of the heart, lungs, or blood vessels.