[en] Ray techniques are used to examine the range of validity of the Doppler shift formula Δf = (-f/sub T//c) dP/dt where f/sub T/ is the transmitter frequency and P the phase path. The simple formula may be used when the time scale of changes in the medium and transmitter and receiver positions is sufficiently large. However, it may fail for quite moderate rates of change. For a moving transmitter a more accurate analysis shows that there may be additional solutions, associated with the complex and ''faster than light'' Doppler effects, which it does not predict. Space-time rays are used to obtain formulas valid in the case where the time scale of the changes, though still large in comparison to the reciprocal of the wave frequency, is not large compared with the time characterizing the wave propagation from transmitter to receiver