Acoustic continuous-wave measurements are presented, which were carried out during June 1978 in the North Sea at a water depth of 30 m. The source was operated at a frequency of 295 Hz and the signal was recorded by two hydrophones at a distance of 1100 m south and east, respectively, from the source. The observed fluctuations of the acoustic amplitude and phase are analysed for periods from 10 min up to 2 hours and are compared with simultaneously measured currents. A theory is developed with the objective of relating the acoustic fluctuations to motions of the sea. For the considered periods and the density stratification during the experiment it is assumed that the observed currents are due to internal waves. The theoretical results agree well with the measurements.