Proton field-cycling nuclear magnetic resonance relaxometry is used to study the spin-lattice relaxation dispersion of selected standard smectic A liquid crystals at different temperatures. Relaxation features at both, in the presence and absence of a monochromatic ultrasonic field are considered. We show that the laboratory-frame spin-lattice relaxation time is mainly governed by traslational diffusion. Order director fluctuations (ODF) are less important while rotational difussion seems to be only relevant near the clearing point. Our study suggests that sonication enhances the ODF contribution in the SmA mesophase. Within the framework of the approach we have outlined, different features associated with the ODF mechanism can be investigated.(C) 2004 American Institute of Physics.