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