An analysis of the classical Doppler effect

Abstract

The Doppler effect is a phenomenon which relates the frequency of the harmonicwaves generated by a moving source with the frequency measured by an observermoving with a different velocity from that of the source. The classicalDoppler effect has usually been taught by using a diagram of moving spheres(surfaces with constant phase) centred at the source. This method permits aneasy and graphical interpretation of the physics involved for the case inwhich the source moves with a constant velocity and the observer is atrest, or the reciprocal problem (the source is at rest and the observermoves). Nevertheless it is more difficult to demonstrate, by this method, therelation of the frequencies for a moving source and observer. We presentan easy treatment where the Doppler formulae are obtained in a simpleway. Different particular cases will be discussed by using this treatment.