Laser-Doppler-anemometry measurements of instantaneous acoustic particle velocity are presented. The Doppler signals, from measurements in air, display quasi-periodic amplitude modulation with a fundamental frequency equal to the frequency of the acoustic field. This effect can cause signal-processing problems. Periodic amplitude modulation is investigated by studying the power spectral densities of the envelopes of measured Doppler signals. Various seeding and acoustic conditions are considered. It is shown that the periodic amplitude modulation is much more significant with water-droplet seeding than it is with smoke-particle seeding. Random amplitude modulation replaces periodic amplitude modulation when a significant steady flow is superimposed on the acoustic field. The harmonic content of the Doppler-signal envelope increases with the intensity of the acoustic field. A simple computational model is used to simulate Doppler-signal envelopes. The simulation is in good qualitative agreement with many experimental observations. However, there is is some discrepancy with experimental measurements, notably a 90° phase difference between the positions of measured and simulated envelope maxima. The paper briefly considers the possibility of exploiting the periodic amplitude modulation effect in a new type of anemometer for acoustic velocity measurement in sound fields with low acoustic frequency and high acoustic particle velocity amplitude.