We present the dynamic velocity profiles of a Newtonian fluid (glycerol) and a viscoelastic Maxwell fluid (CPyCl-NaSal in water) driven by an oscillating pressure gradient in a vertical cylindrical pipe. The frequency range explored has been chosen to include the first three resonance peaks of the dynamic permeability of the viscoelastic-fluid¿pipe system. Three different optical measurement techniques have been employed. Laser Doppler anemometry has been used to measure the magnitude of the velocity at the center of the liquid column. Particle image velocimetry and optical deflectometry are used to determine the velocity profiles at the bulk of the liquid column and at the liquid-air interface respectively. The velocity measurements in the bulk are in good agreement with the theoretical predictions of a linear theory. The results, however, show dramatic differences in the dynamic behavior of Newtonian and viscoelastic fluids, and demonstrate the importance of resonance phenomena in viscoelastic fluid flows, biofluids in particular, in confined geometries.