Doppler shift experiments with source in periodic motion: Parametrized Doppler shift formulas

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.