We present 82 h of high-speed Johnson B photometry, acquired on 21 nights during 1991. A frequency analysis of these data shows that HD 12932 pulsates with a single mode with a frequency of 1436.2986 +/- 0.0013 mu Hz. The first harmonic of this frequency is also detectable, indicating that the oscillations have a non-sinusoidal character. We do not confirm a 3.5295-d amplitude-modulation period presented in an earlier study. We also present differential mean light UBVRI observations of HD 12932, acquired on 21 nights from late 1991 to early 1992 for the purpose of searching for a rotation period. A frequency analysis of these observations does not reveal any significant variations. We identify an error of pi rad in the phases of some of the light curves reported in the earlier study. Once those data are corrected, they yield results in agreement with our own. The (O - C) diagram of all the available data reveals phase variations on a time-scale of several hundred days, a phenomenon already identified in seven other roAp stars. In those stars, the phase changes are attributed to cyclic variations in the frequency of the pulsations. In anticipation of similar behaviour in HD 12932, we argue that long-term monitoring of its pulsation phase is warranted.