A tool generates signals indicative a shear wave slowness of the formation surrounding a borehole. The tool comprises a collar portion adapted for mounting in a drill string, a quadrupole sonic transmitter mounted to the collar portion, and a quadrupole sonic receiver array mounted to the collar spaced apart from the transmitter. A method determines shear wave slowness of the formation. The method includes propagating quadrupole wave energy into the formation and detecting quadrupole dispersive waveform received at a second location. Formation shear wave slowness is calculated using dispersive slowness time coherence processing.