A method for determining mud slowness of a mud in a borehole includes determining slowness as a function of frequency for at least one fluid mode from a set of measurements acquired with a sonic tool in the borehole; and determining the mud slowness from the slowness as a function of frequency for the at least one fluid mode. A downhole sonic tool includes a transmitter capable of generating signals covering a frequency range, a high end of which is more than 30 KHz; and a receiver array comprising a plurality of receivers, which are responsive to the frequency range of the transmitter, wherein the transmitter and the receiver array are spaced apart on a tool body at a selected TR spacing.