  Doppler shift formulas are derived for two less studied scenarios: stationary
receiver and source in harmonic oscillatory motion and stationary receiver and
source in uniform circular motion. For each of the scenarios we derive a
formula, one which works when the emission period is small enough that it can
be considered that two successive signals are emitted from the same point in
space (locality assumption) and another which takes into account that two
successive signals are emitted from two different points in space (non-locality
assumption). The results furnished by the two Doppler shift formulas are
compared, showing that increasing the emission frequency decreases the
difference between the results obtained with the two formulas.
