According to one embodiment of the present invention, the apparatus comprises a first filter for measuring a pressure field at a first axial location along the pipe and providing a first pressure signal indicative of the vortical pressure field. The apparatus further comprises a second filter for measuring the vortical pressure field at a second axial location along the pipe and providing a second pressure signal indicative of the vortical pressure field. The apparatus further comprises a signal processor, responsive to the first and the second pressure signals, which provides a velocity signal indicative of a velocity of the vortical pressure field moving in the pipe.